Question

What should be the annual rate of compound interest in order to earn $1,025 on a principal of $10,000 in 2 years?​

Answer 1

Answer:

5%

1st year

10000 x5% = 500

2nd year

10500 x5% = 525

total 1025

Answer 2

Given,

Principal = $10000,

Compound interest = $1025,

Time = 2 years.

To find,

Rate of interest.

Solution,

Compound interest is defined as the interest earned on the initial principal as well as on the interest accrued from previous periods.

Compound interest, when compounded annually, is given by,

$CI=P[(1+\frac{r}{100} )^t-1],$

Where,

P = Initial principal,

r = rate of interest (%),

t = time period (years)

Substituting the respective values in the above formula, for the given problem,

$1025=10000[(1+\frac{r}{100} )^2-1]$

Rearranging and simplifying,

$(1+\frac{r}{100})^2=\frac{1025}{10000} +1$

⇒ $(1+\frac{r}{100})^2=1.1025$

⇒ $(1+\frac{r}{100})=\sqrt{ 1.1025}$

⇒ $(1+\frac{r}{100})=1.05$

⇒ $\frac{r}{100} =0.05$

⇒ r = 5%

Therefore, the annual rate of interest will be 5%.