Question

A local furniture store is advertising a deal in which you buy a $3,700 dining room set and do not need to pay for two years (no interest cost is incurred). How much money would you have to deposit now in a savings account earning 4 percent APR, compounded monthly, to pay the $3,700 bill in two 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 $ per month = ?

Answer 1

Dining Table Price = $ 3700, Interest Rate = 4 % APR compounded monthly, Monthly Interest Rate = (4/12) = 0.33 % per month

Let the required initial deposit be $ P. This amount when deposited now and kept in the account earning 0.33 % per month should equal the dining room set's price two years from now

Therefore, P x (1.0033)^(12 x 2) = 3700 ( 12 x 2 = 24 is the number of months in two years as compounding is done monthly)

P = 3700 / (1.0033)^(24) = $ 3418.7097 ~ $ 3418.71

If the deposits were to be in the form of equal monthly (end of the month) payments, then the total future value of these deposits compounded at the monthly rate of 0.33 % per month should equal the dining room set's price in two years or 24 months time.

Let the equal monthly deposits be $ K

Therefore, K x (1.0033)^(23) + K x (1.0033)^(22) + ........+ K x (1.0033) + K = 3700

K x [{(1.0033)^(24)-1}/{1.0033 - 1}] = 3700

K x 24.933 = 3700

K = 3700 / 24.933 = $ 148.3963 ~ $ 148.4