Question

A newly formed band would like to buy all new instruments from Sounds Inc. In order to have a down payment for the instruments, the band decides to deposit $500 each quarter in an account that earns 2.02% per year compounded quarterly for 2 years. How much will the band have for a down payment for the new instruments in 2 years

Answer 1

Answer:

The answer is $103,080.32

Explanation:

To calculate this , the formula for a sinking fund, compounded periodically is applied and the formula is stated as follows:

$FV=PMT\frac{(1+\frac{r}{n} )^{n*t}}{\frac{r}{n}}-1$

where:

FV = future value

PMT = periodic payment = $500

r = interest rate = 2.02% = 0.0202

n = number of compounding periods per year = quarterly = 4

t = period of investment in years = 2 years

$FV=500\frac{(1+\frac{0.0202}{4} )^{4*2}}{\frac{0.0202}{4}}-1$

$=500\frac{(1.00505)^8}{0.00505} -1\\= 500(206.162639)-1$

= $103,080.32