Question

Judd is launching a new small-business venture and needs to purchase some equipment. A supplier offers him a deal whereby he can pay $250,000 two years from now for the equipment. Starting three months from now, Judd plans to deposit a fixed amount every quarter (i.e., every three months) in a bank account, so that at the end of two years the account holds exactly $250,000. If the account pays 5.5% APR with monthly compounding, how much must Judd deposit every quarter?

Answer 1

- Future value of amount required in 2 years = $250,000

Judd will deposit an amount at the end of each quarter for 2 years.

Interest rate(APR) = 5.5% monthly compounding

Calculating Effective Quarterly Interest Rate from APR monthly compounding:-

Effective Quarterly Interest Rate

where, r = Interest rate = 5.5%

n= no of periods for Quarterly Effective interest rate = 3

m = no of times compounding in a year = 12

Effective Quarterly Interest Rate

Effective Quarterly Interest Rate

Effective Quarterly Interest Rate = 1.3813%

Now, Calculating the Periodic Quarterly deposit using FV of ordinary annuity formula:-

Where, C= Periodic Payments

r = Periodic Interest rate = 1.3813%

n= no of periods = 2 years*4 = 8

C = $29,770.29

So, the amount Judd deposit every quarter is $29,770.29