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

r = 9.86%

Step-by-step explanation:

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

`FV=PV(1+(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+(r)/(1))^(5)`

dividing both sides by 10,000

`(16000)/(10000) =(10000(1+(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%