Question

Saved Problem 4 and 5-5 Present Value and Annuity Payments A local furniture store is advertising a deal in which you buy a $2,000 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 6 percent APR, compounded monthly to pay the $2.000 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 24 of 46 ! Next >

Answer 1

Formula to calculate present value of lumpsum payment
Present value	Future amount*(1/((1+r)^n)
r is interest rate and n is number of years
Calculation of annual effective interest rate
Effective rate of interest	(1+((r/n)^n)-1
Effective rate of interest	(1+((0.06/12)^12)-1
Effective rate of interest	1.061678-1
Effective rate of interest	6.17%
Using the present value formula we can calculate the amount to be deposited today
Present value	2000*(1/((1+0.06167)^2)
Present value	2000*0.887186
Present value	$1,774.37
Formula to calculate present value of annuity
Present value of annuity	Annuity payment*(1-(1+r)^-n)/r
Monthly interest rate	0.50%	6%/12
Number of payments	24	12*2
Using the above formula we can calculate monthly savings
Annuity amount	2000/(1-(1+0.005)^-24)/0.005
Annuity amount	2000/22.56287
Annuity amount	$88.64
Thus, annuity payment $88.64 per month