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

The answer is $103,080.32

Step-by-step explanation:

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

`FV=PMT((1+(r)/(n) )^(n*t))/((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((1+(0.0202)/(4) )^(4*2))/((0.0202)/(4))-1`

`=500((1.00505)^8)/(0.00505) -1\\= 500(206.162639)-1`

= $103,080.32