Question

You can purchase an appliance (refrigerator, furnaces, A/C, etc.) maintenance contract. You can pay $1,000 today for a year's maintenance coverage or pay $90 per month, each month, starting today, for 12 months.

If your investments earn 5.00% APR (compounded monthly), how much would you save or would it cost you (in present value terms) to pay on a monthly basis?

1.	You would save $81.04

2.	You would lose $55.69

3.	You would save $55.69

4.	You would lose $81.04

5.	You would save $51.31

6.	You would lose $51.31

Answer 1

2. You would lose $55.69.

1st option is to pay $1,000 now itself.

2nd option to pay $90 per month for 12 months.

let us find out the present value of the series of $90 payments.

since first payment is made today, this annuity is in the form of annuity due.

P [ 1 - (1+r)^(-n) / r ] *(1+i)

here,

P = $90.

r = interest = 5% / 12 months

=>0.4166% per month =>0.004166.

n = 12 months.

=> present value of payments = $90*[ [1 - (1.004166)^(^-12)] / 0.004166] * (1.004166)

=>$90*11.729936

=>$1,055.69.

by opting for installments of $90 per month you would be paying (1055.69 -1000) =>$55.69 extra.