Question

1. A bookstore offers you the following deal: you pay $36 today (in January) and you get 5%

off the price of everything you purchase in December (for simplicity assume exactly 12

months from now). If your savings account earns 4.03% APR (compounded monthly), how

much do you have to buy in December to just break even on the offer?

2.

You expect that you will need to replace your furnace in 3 years at a cost of $16,944. How

much must you save, each month for 19 months, starting next month (the same amount

each month) if your savings account pays 2.05% APR (compounded monthly)?

Answer 1

Part 1:

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$                 36.00
Int Rate	0.3358%
Periods	12

Future Value = Present Value * ( 1 + r )^n
= $ 36 ( 1 + 0.003358) ^ 12
= $ 36 ( 1.003358 ^ 12)
= $ 36 * 1.0411
= $ 37.48

Books to be purchased = FV in Dec / Disc Rate

= $ 37.48 / 5%

= $ 749.60

Part 2:

Amount Required in 19 Months :

Particulars	Amount
Future Value	$            16,944.00
Int Rate	0.1708%
Periods	16

Present Value = Future Value / ( 1 + r )^n
= $ 16944 / ( 1 + 0.0017 ) ^ 16
= $ 16944 / ( 1.0017 ) ^ 16
= $ 16944 / 1.0277
= $ 16487.52

Amount Required each Month:

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
FV of Annuity	$         16,487.52
Int Rate	0.1708%
Periods	19

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$16487.52 = Cash Flow * [ [ ( 1 + 0.0017 ) ^ 19 ] - 1 ] / 0.0017
$16487.52 = Cash Flow * [ [ ( 1.0017 ) ^ 19 ] - 1 ] / 0.0017
$16487.52 = Cash Flow * [ [ ( 1.033 ] - 1 ] / 0.0017
$16487.52 = Cash Flow * [ 0.033 ] / 0.0017
Cash Flow = $ 16487.52 * 0.0017 / 0.033
Cash Flow = $ 854.5

Monthly saving is required is $ 854.5