Question

Chris has $3,000 to invest. His brother approached him with an investment opportunity that could double his money in 7 years. What interest rate would the investment have to yield in order for Chris’s brother to deliver on his promise?

Answer 1

Here we have two alternatives

Alternative -1 )

This is when pour investment fetch simple interest

The formula for simple interest is P*r *t

Where t is the time r is interest rate t is the time period

Given that the investment doubles that means

Interest to be earned should be equal to principal amount

3000* (r) * 7 = 3000

r = 1/7

r = 14.2857%

That means if it is simple interest it should be 14.2857% per annum

Alternative -2)

When it is Compound Interest

We know the future value of investment for compound interest is

P *(1+r)^t

Where P is the investment r is the rate of interest t is the time period

Given double the amount hence,

6000 = 3000 *(1+r)^7

(1+r)^7 = 2

1+r = 1.10409

r = 10.40895%

Hence if the investment is compounded annually the interest rate should be 10.40895%