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

Answer:

Jason borrowed $4,4,77.29

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:

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

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

$6,000\ =\ PV(1+\frac{0.1}{2} )^{(2\times 3)}\\6,000\ =\ PV(1+ 0.05)^{6}\\6,000\ =\ PV(1.05)^{6}\\6,000\ =\ PV (1.340096)\\diving\ both\ sides\ by\ 1.340096\\PV = \frac{6,000}{1.340096} \\PV = \ 4,477.29$

Therefore, Jason borrowed $4,4,77.29