Question

Suppose you are committed to owning a $250,000 Ferrari and you have $100,000 now. If you believe your mutual fund can achieve a 12 percent annual rate of return and you are able to save $1000 per month, how long you will have to wait for buying the car?

	A.	5.3 years
	B.	3.5 years
	C.	8.6 years
	D.	4.7 years

Answer 1

Given,

Future value = $250000

Current amount = $100000

Annual rate of return = 12% or 0.12

Monthly savings = $1000

Solution :-

Monthly rate (r) = 0.12/12 = 0.01

Let number of months be 'n'

Future value = Current amount x (1 + r)ⁿ + Monthly savings/r x [(1 + r)ⁿ - 1]

$250000 = $100000 x (1 + 0.01)ⁿ + $1000/0.01 x [(1 + 0.01)ⁿ - 1]

$250000 = $100000 x (1.01)ⁿ + $1000/0.01 x (1.01)ⁿ - $1000/0.01

$250000 + $1000/0.01 = $100000 x (1.01)ⁿ + $1000/0.01 x (1.01)ⁿ

$250000 + $100000 = (1.01)ⁿ x [$100000 + $1000/0.01]

$350000 = (1.01)ⁿ x [$100000 + $100000]

$350000 = (1.01)ⁿ x $200000

$350000/$200000 = (1.01)ⁿ

1.75 = (1.01)ⁿ

Taking 'Log' both sides,

Log(1.75) = Log(1.01)ⁿ

Log(1.75) = n.Log(1.01)

0.55961578794 = n.(0.00995033085)

0.55961578794/0.00995033085 = n

56.24 = n

So, number of months are 56.24

Now,

Number of years = 56.24/12 = 4.7 years

You will have to wait 4.7 years for buying the car.