Question

Three years from now you need to pay a loan (onetime) of $6,000. Also, you have planned to buy a car with $15,000 then. Now you work for an NGO (no pay) in the Amazon forest, and expect to get a reward of $10,000 after three years of service. How much money do you have to put now in a bank at 9% interest (compound). so that you meet these two expenses after 3 years? A.. $9, 090 B. 3, 090 C. . $8,494 D. $2,494

Answer 1

Answer - "C". $8,494

Here, we need to calculate the present value of the amount that we would require in future to meet the expense.

Amount that we required to invest today for meeting our future obligation will be the present value of net cash required at the end of 3rd year.

Net Cash Required at the end of 3rd year = Cash Outflow - Cash Inflow

i.e Payment for Loan + Payment for Car - Reward from NGO

= $6,000 + $15,000 - $10,000

= $11,000

Therefore $11,000 will be the fund that we will require at the end of 3rd year but if need to calcualte the amount we required today to invest to meet the future obligation we need to get the present value of the amount that we would be required to pay at the end of 3rd year.

Rate - 9%

Calcualtion of Present Value Factor = 1 / (1 + 0.09)^3

Calculation of Present Value = Future Value * Present Value Factor

Future Value = $11,000

Present Value Factor = 0.7722

Present Value = $11,000 * 0.7722

= $8,494 (round off to nearest decimal)

For breif calculation refer the below table -

A B A+B Net Cash Year Particular Cash Outflow Cash Inflow Flow PVF@9% PV 3 Loan Payment $ (6,000.00) $ $ (6,000.00) 0.7722 $ (4,633.10) 3 Car Payment $ (15,000.00) $ $(15,000.00) 0.7722 $(11,582.75) 3 Reward from NGO $ $ 10,000.00 $ 10,000.00 0.7722 $ 7,721.83 Net Cash Required $(11,000.00) $ (8,494.00)