Question

Today is date 0. In 10 years, you plan to retire and buy a house in Norman, OK. In terms of a time line, you will retire at the end of year 10. The house you are looking at currently costs $200,000 and is expected to increase in value each year at a rate of 5% compounded annually. Assuming you can earn 10% annually on any investment you might make, how much must you invest at the end of each of the next 10 years to be able to buy your dream home when you retire?

Group of answer choices

$12,177

$20,441

$12,343

$14820

$16,188

Answer 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 growth rate per period
n - No. of periods

Particulars	Amount
Present Value	$         200,000.00
Int Rate	5.0000%
Periods	10

Future Value = Present Value * ( 1 + r )^n
= $ 200000 ( 1 + 0.05) ^ 10
= $ 200000 ( 1.05 ^ 10)
= $ 200000 * 1.6289
= $ 325778.93

Price after 10 Years is $ 325778.93

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	$      325,778.93
Int Rate	10.0000%
Periods	10

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$325778.93 = Cash Flow * [ [ ( 1 + 0.1 ) ^ 10 ] - 1 ] / 0.1
$325778.93 = Cash Flow * [ [ ( 1.1 ) ^ 10 ] - 1 ] / 0.1
$325778.93 = Cash Flow * [ [ ( 2.5937 ] - 1 ] / 0.1
$325778.93 = Cash Flow * [ 1.5937 ] / 0.1
Cash Flow = $ 325778.93 * 0.1 / 1.5937
Cash Flow = $ 20441.13

Annual deposit required is $ 20441.

Option B is correct.