Question

1a.) During 2008 the S&P 500 index depreciated by 37.6%.† Assuming that this trend had continued, how much would a $6,000 investment in an S&P index fund have been worth after 9 years? (Round your answer to the nearest cent.)

1b.)

A $4,000 loan, taken now, with a simple interest rate of 7% per year, will require a total repayment of $6,240. At what time t will the loan mature?

Answer 1

Part 1a):

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	$            6,000.00
Int Rate	-37.6000%
Periods	9

Future Value = Present Value * ( 1 + r )^n
= $ 6000 ( 1 + -0.376) ^ 9
= $ 6000 ( 0.624 ^ 9)
= $ 6000 * 0.0143
= $ 86.06

Amount will be $ 86.06 after 9 Years.

Part 1b):

Int = Maturity Value - Loan

= $ 6240 - $ 4000

= $ 2240

Maturity Time = Int / [ Principal * Int rate ]

= $ 2240 / [ $ 4000 * 7% ]

= $ 2240 / $ 280

= 8

It takes 8 Years time to earn $ 2240 Int.