Question

Problem 4 and 5-6 Present Value and Annuity Payments

A local furniture store is advertising a deal in which you buy a $4,400 living room set with three years before you need to make any payments (no interest cost is incurred).

How much money would you have to deposit now in a savings account earning 6 percent APR, compounded monthly, to pay the $4,400 bill in three years? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Present value

$

How much would you have to deposit in the savings account each month to be able to pay the bill? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Annuity payment

$

Answer 1

Answer a.

Amount to be paid in 3 years = $4,400
APR = 6%
Monthly Interest Rate = 6%/12 = 0.5%

Present Value = Amount paid / (1 + monthly interest)^time
Present Value = $4,400 / 1.005^36
Present Value = $3,676.84

You need to deposit $3,676.84 today so that you can have $4,400 after 3 years

Answer b.

Amount to be paid in 3 years = $4,400
APR = 6%
Monthly Interest Rate = 6%/12 = 0.5%

Monthly Payment * FVIFA(0.5%, 36) = $4,400
Monthly Payment * (1.005^36 - 1) / 0.005 = $4,400
Monthly Payment * 39.3361 = $4,400
Monthly Payment = $111.86

So, you need to deposit $111.86 monthly