Question

Use the following formula for compound interest. If P dollars is invested at an annual interest rate r (expressed as a decimal) compounded n times yearly, the amount A after t years is given by

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

Required:
What rate of interest is required so that $1000 will yield $1900 after 5 years if the interest rate is compounded monthly?

Answer 1

12.906%/year

Explanation:

Given data

Principal= $1000

Final Amount= $1900

Time= 5 years

The compound interest formula is given as

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

Solving for rate r as a decimal

r = n[(A/P)1/nt - 1]

r = 12 × [(1,900.00/1,000.00)1/(12)(5) - 1]

r = 0.12906

Then convert r to R as a percentage

R = r * 100

R = 0.12906 * 100

R = 12.906%/year