Alif deposited RM2500 in Bank Delima at the beginning of 2019 with an annual interest rate of 4%. We need to calculate the maturity value Alif receives at the end of 2024 if the interest is compounded (a) annually and (b) every 3 months.

1. Problem Description

Alif deposited RM2500 in Bank Delima at the beginning of 2019 with an annual interest rate of 4%. We need to calculate the maturity value Alif receives at the end of 2024 if the interest is compounded (a) annually and (b) every 3 months.

2. Solution Steps

(a) Compounded annually:

The formula for compound interest is:

$A = P (1 + r/n)^{nt}$

where:

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (as a decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for

In this case:

$P = 2500$

$r = 0.04$

$n = 1$

$t = 2024 - 2019 = 5$

$A = 2500 (1 + 0.04/1)^{(1*5)}$

$A = 2500 (1 + 0.04)^{5}$

$A = 2500 (1.04)^{5}$

$A = 2500 * 1.2166529024$

$A = 3041.632256$

$A \approx 3041.63$

(b) Compounded every 3 months:

In this case:

$P = 2500$

$r = 0.04$

$n = 12/3 = 4$

$t = 2024 - 2019 = 5$

$A = P (1 + r/n)^{nt}$

$A = 2500 (1 + 0.04/4)^{(4*5)}$

$A = 2500 (1 + 0.01)^{20}$

$A = 2500 (1.01)^{20}$

$A = 2500 * 1.22019004$

$A = 3050.4751$

$A \approx 3050.48$

3. Final Answer

(a) If the interest is compounded annually, Alif will receive RM3041.63 at the end of

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4. (b) If the interest is compounded every 3 months, Alif will receive RM3050.48 at the end of

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4. The more frequently the interest is compounded, the higher the maturity value.