Question

An account had an initial deposit made and then interest was applied once a year at a fixed rate. The amount of money, in dollars, in the account after t years, was 103(1.02) t . What was the annual interest rate?

Answer 1

The annual interest rate is 20%.

Explanation:

Since, we know that,

If an sum of money P is increasing yearly at a fixed rate,

Then the amount after t years,

`A=P(1+r)^t`

Where, r is the annual rate,

t is the number of years,

Here, the given amount after t years,

`A'=103(1.02)^t`

By comparing,

1 + r = 1.02

⇒ r = 0.02 ( Subtracting 1 on both sides )

⇒ r = 20 %

Hence, the annual interest rate is 20%.

Answer 2

Amount in compound interest = p(1 + r/t)^nt where p is the initial deposit, r = rate, t = number of compunding in a period and n = period.

Here, Amount after t years = 103(1.02)^t
i.e. 1 + r = 1.02
r = 1.02 - 1 = 0.02
Therefore, annual interest rate = 0.02 x 100 = 2%