Question

Jack asked Jill to marry him, and she has accepted under one condition: Jack must buy her a new

$310,000

Rolls-Royce Phantom.  Jack currently has

$28,310

that he may invest.  He has found a mutual fund with an expected annual return of

5.5

percent in which he will place the money.  How long will it take Jack to win Jill's hand in marriage?  Ignore taxes and inflation.

The number of years it will take for Jack to win Jill's hand in marriage is

nothing

years.  (Round to one decimal place.)

Answer 1

FV = PV * (1+annual rate)^N

330000 = 59680 * (1+4%)^N

(1+4%)^N = 330000/59680

(1+4%)^N = 5.529491

Taking LOG in both sides,

N x LN(1.04) = LN(5.529491)

N * 0.039221 = 1.710096

N = 1.710096/0.039221

N = 43.6 years

Answer 2

SOLUTION :

Let n years be taken to be able to buy a car worth 310,000  by investing today $28310 at the interest rate of 5.5% .

So, 

FV = $310000

PV = 28310 

r = 5.5% = 0.055

=> 1 + r = 1.055

We know that :

FV = PV (1 + r)^n

=> 310000 = 28310 * 1.055^n

=> 1.055^n = (310000/28310) = 10.9502

Taking log :

=> n log(1.055) = log(10.9502)

=> n = log(10.9502) / log(1.055)

=> n = 44.70 years.

So,

The number of years it will take  for Jack to win Jill’s hand in in marriage is

= 44.70 years (ANSWER).