Question

A condominium in Maui now costs $500,000. Inflation is expected to cause this price to increase at 8 percent per year over the next 5 years before you retire from your CFO position in a Big 4 company. How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 12 percent to buy the condominium upon retirement?

	A)	$115,643.27
	B)	$153,717.02
	C)	$103,252.92
	D)	$92,313.56
	E)	$125,228.23

Answer 1

Step 1
Calculate the price of condominium after 5 years i.e. on your retirement.
We can use the future value of sum formula to calculate this price.
Future value of sum = P x (1+r)^n
Future value of sum = price of condominium at the end of 5th year = ?
P = Present price of condominium = $500000
r = inflation rate = 8%
n = no.of years = 5
Future value of sum = 500000 x (1+0.08)^5 = 734664
Price of condominium at the end of 5th year = $7,34,664
Step 2
Calculation of equal annual end-of-year deposit must be made into an account
paying an annual rate of interest of 12 percent to buy the condominium upon retirement
We can use the future value of annuity formula to calculate this annual deposit amount.
Future value of annuity = P x {[(1+r)^n -1]/r}
Future value of annuity = price of condominium at the end of 5th year = $7,34,664
P = Annual deposit into account = ?
r = rate of interest per annum = 12%
n = no.of years = 5
734664 = P x {[(1+0.12)^5 -1]/0.12}
734664 = P x 6.352847
P = 115643.27
Annual end of deposit required = $1,15,643.27
The answer is Option A.