Profits and costs of depositing and borrowing money

Profits and costs of depositing and borrowing money

In business, you can deposit money or secure a loan from banks, micro financial institutions, SACCOS or individuals offering financial services. If you deposit money for a specified period of time, you will generate profit depending on the amount of money deposited. The profit generated is called interest. Profit is computed basing on the interest rate paid by the service provider. You can also secure a loan for business purposes. The loan will be repaid with an interest based on the agreed interest rate and fixed time period.

Interest (I), interest rate (R), time (T) and principal (P) in bank deposits. In this section, you will learn how to solve word problems on profit. Besides, you will learn about interest (I), interest rate (R), time (T), and principal (P). The amount of money deposited in a bank for business is called principal. The principal generates a profit which is called interest, when deposited in bank for a fixed period of time. The annual interest rate is given in percentage. A person who deposits money in the bank expects to earn interest based on the amount of money deposited. The interest (I) earned depends on the principal (P), interest rate (R), and the fixed time (T).

Computations of interest, interest rate, time, and principal. Interest generated from bank deposits is computed by using the following formula:

$I = \frac{P \times R \times T}{100}$

Or, in short form: $I = \frac{PRT}{100}$

By using this formula, you can get the formulae for other variables as follows.

Variable	Formula
Interest (I)	$I = \frac{PRT}{100}$
Interest rate (R)	$R = \frac{100I}{PT}$
Principal (P)	$P = \frac{100I}{RT}$
Time (T)	$T = \frac{100I}{PR}$

Example 1

Find the interest earned after depositing 40,000 shillings in a bank at an interest rate of $10\frac{1}{2}\%$ per year for 4 years.

Solution

Given: Principal, $P = \text{sh } 40,000$

Interest rate, $R = 10\frac{1}{2}\%$ or $\frac{21}{2}\%$

Time, $T = 4$ years

By using the formula for computing interest: $I = \frac{PRT}{100}$

Substitute in the formula all values of variables as follows:

$I = \frac{40,000 \times \frac{21}{2} \times 4}{100}$

$= \frac{40,000 \times 21 \times 2}{100}$

$= \text{sh } 16,800$

Therefore, the interest earned was 16,800 shillings.

Example 2

Amina deposited 200,000 shillings in a bank. If the bank pays an annual interest rate of $7\frac{1}{2}\%$, how long did it take for her to earn an interest of 45,000 shillings?

Solution

Given: $P = \text{sh } 200,000$, $I = \text{sh } 45,000$, $R = 7\frac{1}{2}\% = \frac{15}{2}\%$, $T = ?$

By using the formula for computing time: $T = \frac{100I}{PR}$

Substitute in the formula all values of variables as follows:

$T = \frac{100 \times 45,000}{200,000 \times \frac{15}{2}}$

$T = 3$ years

Therefore, Amina received an interest of 45,000 shillings after 3 years.

Example 3

Sekela deposited money in a bank that pays an annual interest rate of 10%. If she received an interest of 21,600 shillings after 3 years, how much money did she deposit?

Solution

Given: $I = \text{sh } 21,600$, $T = 3$ years, $R = 10\%$, $P = ?$

By using the formula for computing principal: $P = \frac{100I}{RT}$

Substitute the values of variables in the formula as follows:

$P = \frac{100 \times 21,600}{10 \times 3}$

$= \text{sh } 72,000$

Therefore, Sekela deposited 72,000 shillings.

Example 4

An amount of 360,000 shillings was deposited in a bank. An interest of 129,600 shillings was generated after 4 years. What is the interest rate paid by the bank per year?

Solution

Given: $P = \text{sh } 360,000$, $I = \text{sh } 129,600$, $T = 4$ years, $R = ?$

Using the formula for computing interest rates: $R = \frac{100I}{PT}$

Substitute the values of variables in the formula as follows:

$R = \frac{100 \times 129,600}{360,000 \times 4}$

$= 9\%$

Therefore, the bank pays an annual interest rate of 9%.