Answer :

The compound interest on an investment of 3600 for 4 years at an annual interest rate of 3% is approximately 451.83 units of currency.

To find the compound interest on an investment of 3600 for 4 years at an annual interest rate of 3%, we can use the compound interest formula:

[tex]\[A = P \times \left(1 + \frac{r}{n}\right)^{nt}\][/tex]

Where:

- (A) is the future value of the investment,

- (P) is the principal amount (initial investment),

- (r) is the annual interest rate (in decimal),

- (n) is the number of times interest is compounded per year, and

- (t) is the time the money is invested for in years.

Given:

- (P = 3600),

- (r = 0.03) (3% interest rate expressed as a decimal),

- (t = 4) years, and

- Since the compounding frequency is not specified, we assume it's compounded annually, so (n = 1).

Substituting the values into the formula:

[tex]\[A = 3600 \times \left(1 + \frac{0.03}{1}\right)^{1 \times 4}\][/tex]

[tex]\[A = 3600 \times \left(1 + 0.03\right)^4\][/tex]

[tex]\[A = 3600 \times (1.03)^4\][/tex]

[tex]\[A = 3600 \times 1.12550857\][/tex]

[tex]A =4051.82965[/tex]

Now, to find the compound interest, we subtract the initial investment from the future value:

[tex]\[\text{Compound interest} = A - P\][/tex]

[tex]\[\text{Compound interest} = 4051.82965 - 3600\][/tex]

[tex]\[\text{Compound interest} = 451.83\][/tex]

This calculation demonstrates the growth of an investment through compounding over time, where the interest earned in each period is added to the principal for the next period's interest calculation.

QUESTION

Find the compound interest on an investment of 3600 for 4 years at an annual interest rate of 3%.

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Rewritten by : Barada