Question

Suppose you borrow $10,000 right now to start a business. If the terms of the loan require you to pay back $16,000 in 5 years, what is the implied annual compound interest rate

Answer 1

Answer:

r = 9.86%

Explanation:

The formula for calculating the future value of an invested amount yielding a compound interest is given by:

$FV=PV(1+\frac{r}{n})^{nt}$

where:

FV = future value = $16,000

PV = present value = $10,000

r = interest rate = ?

n = number of compounding period per year = 1

t = time in years = 5

∴ $16000=10000(1+\frac{r}{1})^{5}$

dividing both sides by 10,000

$\frac{16000}{10000} =\frac{10000(1+\frac{r}{1})^{5}}{10000}$

$1.6 = (1 + r)^{5}$

to remove the power of 5, we have to take the 5th root of both sides:

$(1.6)^{1/5} = (1 + r )^{5 * 1/5}$

Using your calculator:

1.09856 = 1 + r

∴ r = 1.09856 - 1 = 0.09856

r = 0.0986 = 9.86%

∴ r = 9.86%