Question

Jason has a loan that requires a single payment of $6,000 at the end of 3 years. The loan's interest rate is 10%, compounded semiannually. How much did Jason borrow? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Answer 1

Jason borrowed $4,4,77.29

Step-by-step explanation:

In order to calculate this, let we will use the formula for the future value on an invested amount, semiannually, yielding interest at a certain interest rate. This is done as follows:

`FV\ =\ PV(1+(r)/(n) )^((n* t))`

where:

FV = future value = $6,000 (loan repayment)

PV = present value = amount borrowed = ??

r = interest rate = 10% = 10/100 = 0.1

n = number of compounding periods per year = 2

t = time = 3 years

`6,000\ =\ PV(1+(0.1)/(2) )^((2* 3))\\6,000\ =\ PV(1+ 0.05)^(6)\\6,000\ =\ PV(1.05)^(6)\\6,000\ =\ PV (1.340096)\\diving\ both\ sides\ by\ 1.340096\\PV = (6,000)/(1.340096) \\PV = \$4,477.29`

Therefore, Jason borrowed $4,4,77.29