Simple Interest is the interest paid on the original principal amount only. To calculate the simple interest, use the following formula:

Simple Interest = P x r x n; I = Prt

Where: P = Principal,

r = interest rate,

n = term of the loan in years, time the money will be used or

 invested, 

I = Interest.

The amount F in your account after t years is:

F = P + I = P(1 + rt)

Where: F = Future value,

P = Principal,

  r = interest rate,

Example 1:

Let us say that you are borrowing PHP 10,000 from Bank A to finance an automobile purchase. You were quoted a simple interest rate of 5 percent, with a loan term of 5 years. 

Solution: Using the equation, I = Prt, (10,000)(0.05)(5) = PHP 2,500.00

Conclusion: The simple interest amounts to PHP 2,500.00. 

Example 2:

James went to a bank to borrow PHP 100,000 for a gadget he wanted to buy. The bank charges a simple interest rate of 5% and James will repay this loan for a period of 3 years. How much interest does he have to pay?

Solution: Using the equation, I = Prt:

I = (100,000)(0.05)(3 years) = PHP 15,000

  Following the equation to find F,  F = P + I:

F = 100,000 + 15,000 = PHP 115,000

Conclusion: James needs to pay PHP 115,000 to return the amount he borrowed. 

Example 3: 

Suppose Angelle invested PHP 10,000 for 5 years with a simple annual interest of 10%. What is the future value of her investment?

Solution: Using the equation for F, F = P(1 + rt)

F = 10,000 x [1 + (0.10 x 5)] = 15,000

Conclusion: The future value of her investment is PHP 15,000. 

Compound Interest

Compound interest is the interest paid or earned not only on the original principal but also on all interest previously earned. Thus, it is often regarded as “interest on interest.” The formula for calculating the amount of money accumulated after n years, including interest is:

A = P[1 + (r/m)]^mt

Where: P = principal, 

r = the annual rate of interest, 

t = is the number of years the amount is deposited or borrowed for, 

m = is the number of times the interest is compounded per year. 

Remember: 

• When calculating compound interest, the number of compounding periods makes a significant difference. The higher the number of compounding periods, the higher the amount of compound interest.

Compounding Frequency

Number of Compounding periods

Annually: 1

Semi-annually: 2

Quarterly: 4

Monthly: 12

Example 1:

You are taking out a PHP10,000 loan from Bank A, but the 5% interest rate is compounded annually. The loan term is still 5 years. 

Solution: Using the formula, A = P[1 + (r/m)]^mt

A = 10,000[ 1 + (0.05/1)]^(1)(5)

A = 12,762. 82

Conclusion: The loan after 5 years amounts to PHP 12,762.82.

Example 2:

Erika invested PHP50,000 in a bank that pays 8% compounded quarterly for 5 years. How much is her money in the bank after 5 years?

Solution: Using the Formula, A = P[1 + (r/m)]^mt

A = 50,000[1+0.08/4]^(4)(5)

A = 74,297.37.

Interest = A - P

= 74,297.37 - 50,000

Interest = 24,297.37

Conclusion: Erika’s money amounts to PHP 74,297.37 after 5 years, with a total interest of PHP 24,297.37.

Simple interest is easier to calculate and comprehend than compound interest. You will only need to worry about the interest being added to the outstanding principal balance if you have a temporary loan or one with interest that does not compound.

On the other hand, because it allows funds to grow at a faster rate than they would in an account with a simple interest rate, compound interest is better for investing.

Further Understanding exercises (Practice at home): Questions

Questions for Further Understanding: 

1. How long will it take for PHP 4,000 to double if a simple interest of 10% per annum is applied?

2. Let us say you take out a personal loan toward your first home purchase from your family. They graciously lend you PHP 40,000 at a 2 percent interest rate. They say you can pay it back slowly over the next 10 years. What will be the interest after 10 years?

3. Deposit the principal amount of PHP 10,000 into a savings account that pays interest at the rate of 5%. What is the amount in the account after 1 year if the account is:

   1. Compounded annually

   2. Compounded semi-annually

   3. Compounded quarterly

   4. Compounded monthly

4. Julia invested PHP 100,000 in a trust fund that pays 12% compounded semi-annually. How long will it take for Julia to double her money?

Learn More: Future Value and Present Value

Learn More:

• The current value of a future sum of money or stream of cash flows at a certain rate of return is known as present value (PV).

• When regular payments are made and a lump sum is paid at the end of the period, this lump sum is called the future value (FV). 

Time Deposit Account. 

A term deposit is a fixed-term investment that requires money to be deposited into a bank account. Term deposit investments typically have short maturities of one month to few years and varying minimum deposit requirements.

Typically, term deposits offer higher interest rates than basic savings accounts, whereby customers can withdraw their money at any time.

Time Deposits in the Philippines 

In the Philippines, Time Deposits are covered by the Philippine Deposit Insurance Corporation up to PHP500,000.00.

At expiry date, depositors may choose to do the following:

• Withdraw both the principal and the interest earned by the end of the term or the maturity date of the account.

• Take the earnings and re-invest the principal.

• Re-invest both the original principal and the additional income, and  roll it over for the same term. The longer the period, the greater the rate and income.

Time Deposit sample problems 

Example 1:

Jake invests PHP 5,000 in a term deposit scheme. The scheme offers an interest rate of 6% per annum, compounded quarterly. How much interest will Jake earn after one year? Also, what is the effective rate of interest?

Solution: We know that,

• Principal amount = P = Rs. 5,000

• Actual rate of interest = i = 6% p.a. = 0.06 p.a. = 0.015 per quarter

• Number of conversion periods = n = 4 (since we are calculating for one year and compounding happens every quarter)

Therefore, the compound interest (I) is,

I = P x [(1 + i)n – 1] = 5000 x [(1 + 0.015)4 – 1] = 5000 x 0.06136355 = 306.82

Hence, after one year, Jake earns a total interest (I) of PHP 306.82. Further, the effective rate of interest (E) is,

E = (1 + i)n – 1 = (1 + 0.015)4 – 1 = 0.0613 or 6.13%.

Conclusion: Jake will earn PHP 306.82 with an interest rate of 6.13%.

Example 2:

In a bank, an amount of PHP 20,000 is deposited for one year. The rate of interest is 8% per annum and is compounded semi-annually. What is the effective rate of interest?

Solution: To calculate the effective rate of interest, we do not need the amount. 

E = (1 + i)n – 1 … where ‘E’ is the effective rate of interest, ‘i’ is the actual rate of interest in decimal, and ‘n’ is the number of conversion periods.

In this problem, we know that,

• The actual rate of interest = i = 8% p.a. = 0.08 p.a. = 0.04 per semi-year (6 months).

• Number of conversion periods = n = 2 (since we are calculating for one year and compounding happens once every six months)

E = (1 + i)n – 1 = (1 + 0.04)2 – 1 = 1.0816 – 1 = 0.0816 or 8.16%.

Conclusion: Therefore, the effective rate of interest is 8.16%

Money Market Account. 

Money market accounts combine the features of savings and checking accounts. They typically come with debit cards and limited check-writing privileges, as well as interest rates that are typically higher than those of standard savings accounts.

Money Market in the Philippines

Similar to other types of savings accounts, Money Market accounts in the Philippines are also insured by the PDIC.

Steps on solving for interest rates on the money market with sample problem and solution.

Example 1:

If PHP 250,000 is invested in a money market account that has an interest rate of 3.08425% APR, how much is the account balance after a week?

Solution: Step 1: Calculate the daily interest rate for the week. This is done by dividing the  annual percentage rate (APR) by 365 to get the daily interest rate. That is, 

Daily Interest Rate = (APR/365) = 0.0308425 / 365 = 0.0000845

Step 2: Calculate the interest for the first day of the week. This is done by multiplying the initial amount by the daily interest rate. 

Interest = PHP 250,000 x 0.0000845 = 21.125

Step 3: Add the interest earned to the balance in the money market account. Also, add any deposits and deduct withdrawals that you made that day to get the ending balance, which serves as your starting balance for the next day. 

Calculate the starting balance for the second day, 

Starting Balance = PHP 250,000 + 21.13 = PHP 250,021.13

Step 4: Repeat steps 2 and 3 for the remaining days of the week. 

Calculate the interest for the third day, 

Interest = PHP 250,021.13 x 0.0000845 = 21.13

Starting Balance = PHP 250,021.13 + 21.13 = PHP 250,042.26

For the fourth day, 

Interest = PHP 250,042.26 x 0.0000845 = 21.18

Starting Balance = PHP 250,042.26 + 21.18 = PHP 250,063.39

For the fifth day, 

Interest = PHP 250,063.39 x 0.0000845 = 21.13

Starting Balance = PHP 250,063.39 + 21.13 = PHP 250,084.50

For the sixth day, 

Interest = PHP 250,084.50 x 0.0000845 = 21.13

Starting Balance = PHP 250,084.50 + 21.13 = PHP 250,105.63

For the seventh day, 

Interest = PHP 250,105.63 x 0.0000845 = 21.13

Starting Balance = PHP 250,105.63 + 21.13 = PHP 250,126.76

Conclusion: So, in one week, the accumulated amount is PHP 250,126.76. Following the same procedure, the account will be PHP 257,820.56 at the end of 1 year. The total interest earned is PHP 7,820.56.

Disadvantages and advantages of opening a money market account.

Having a money market account has both benefits and drawbacks, especially when compared to other types of accounts. Listed below are the advantages and disadvantages of opening one:

Advantages

• Higher interest rates

• Check-writing privileges

• Debit cards

• Insurance protection

Disadvantages

• Limited transactions

• Fees

• Minimum balance requirement

Stocks and Bonds. 

A stock is a type of security that is mostly sold on stock exchanges and shows that the owner has a share of the company that issued it. Stock units are referred to as "shares," and their owners are entitled to a share of the corporation's assets and profits proportional to their stock holdings.

Explanation of Equity and ownership and how it relates to stocks and bonds

How does stock relate to Equity and Ownership?

A shareholder is considered an owner of the issuing company, determined by the number of shares an investor owns relative to the number of outstanding shares.

When you own stock, you can vote at shareholder meetings, receive dividends if and when they are paid out, and sell your shares to other people.

Steps on how to read stock tables / quotes.

To purchase securities, a mutual fund pools the funds of numerous investors. The manager of the fund purchases securities to implement a specified investment strategy. You will own a portion of the fund's total portfolio of securities, which could include hundreds or a few dozen stocks, if you invest in it.

Types of Mutual Funds and their characteristics 

There are four types of mutual funds according to the investment objective of the fund:

• Stock Funds. This fund primarily invests in stocks or equity, as the name suggests. There are numerous subcategories within this group. Some equity funds are referred to by the size of the businesses in which they invest: large, midsize, or small-cap

• Bond funds. The fixed income category includes a mutual fund with a minimum return. Investments with a fixed rate of return, such as corporate bonds, government bonds, or other debt instruments, are the primary focus of a fixed-income mutual fund.

• Balanced Funds. Balanced funds put their money into a mix of stocks, bonds, money market instruments, and other investments. This fund, also known as an asset allocation fund, aims to lessen exposure to various asset classes.

• Money Market Funds. Short-term, risk-free debt instruments, mostly government Treasury bills, make up the money market. A typical return is slightly higher than that of a typical savings or checking account and slightly lower than that of a typical certificate of deposit (CD).

Balanced fund

Balanced Fund: In a single portfolio, a balanced fund incorporates an equity stock component, a bond component, and occasionally a money market component.

Opening a balanced fund has its advantages and disadvantages, below are some of the following:

Advantages

• Diversified, constantly rebalanced portfolio

• Low expense ratios

• Less volatility

• Low-risk

Disadvantages

• Fixed asset allocations

• Unsuited for tax-shielding strategies

• "The usual suspects" investments

• Safe but stodgy returns

Mutual Fund sample problem/s

The formula used to calculate the Net Asset Value per share for an investment fund is:

NAV = (Assets – Liabilities) / Total number of outstanding shares

Here, the total number of outstanding shares signifies the number of units constituting a fund.

Example 1:

For example, Patricia invests in a mutual fund with 30,000 units. The value of fund assets is worth PHP 20 million. The short-term and long-term liabilities are PHP 2 million and PHP 1 million along with other expenses ,totaling PJP 2 million. She wants to know the Net Asset Value of a mutual fund for 2,000 shares after the tenure ends, considering the market rates and conditions remain the same.

Solution: To calculate Patricia’s return, the first thing required would be to find out per share NAV:

               = {20,000,000 – (2,000,000+1,000,000+2,000,000)} / 30,000

               = (20,000,000 – 5,000,000) / 30,000

               = 15,000,000 / 30, 000

                 = PHP 500

Since, the per unit price of the fund share = PHP 500

Patricia’s NAV, therefore, would be = 500 * 2000 = PHP 1,000,000