AC3059 | Calculating the Present Value of Investments
Questions:
2.After placing $13,000 in a savings account paying annual compound interest of 3%, Leona will accumulate what amount if she leaves the money in the bank for 4 years?
3.Alex Karez has taken out a loan of $180,000 with an annual rate of 10% compounded monthly to pay off hospital bills from his wife’s illness. If the most Alex can afford to pay is $3,500 a month, how long will it take to pay off the loan? How long will it take to pay off the loan if he can pay $4,000 each month? Use five decimal places for the monthly percentage rate in your calculations. If Alex can pay $3,500 a month, how many years will it take to pay off the loan?
4.To pay for your education, you have taken out $28,000 in student loans. If you make monthly payments over 13 years at 5% compounded monthly, how much are your monthly student loan payments?
Answers:
1. Calculating the future value:
|
Particulars |
Value |
|
PMT |
$ 500 |
|
Time |
9 |
|
Rate |
10% |
|
Future Value |
500 * ((((1 + 10%)^9) - 1) / 10%) |
|
Future Value |
$ 6,789.74 |
|
Particulars |
Value | ||
|
PMT |
$ 900 | ||
|
Time |
9 | ||
|
Rate |
10% | ||
|
Future Value |
900 * ((((1 + 10%)^9) - 1) / 10%) |
Future Value |
$ 12,221.53 |
2. Calculating the amount that will be accumulated by Leona:
|
Particulars |
Value |
|
Investment amount |
$ 13,000 |
|
Interest rate |
3% |
|
Time |
4 |
|
Amount |
$ 14,631.61 |
3 Calculating values for Alex Karez:
|
Particulars |
Value |
|
Loan amount |
$ 180,000 |
|
Annual rate |
10% |
|
PMT per month |
$ 3,500 |
|
Months |
19 |
|
Particulars |
Value |
|
Loan amount |
$ 180,000 |
|
Annual rate |
10% |
|
PMT per month |
$ 4,000 |
|
Months |
18 |
Alex will take 1.7 years for paying off the loan with a monthly payment of $3,500.
4. Calculating the monthly student loan payments:
|
Particulars |
Value |
|
Loan Amount |
$ 28,000 |
|
Interest rate |
0.42% |
|
Time |
156 |
|
Monthly payments |
$ 244.46 |
5. Calculating the Present Value of Investments:
|
Discounting rate |
10% | ||||||
|
End of Year |
A |
B |
C |
Dis-rate |
Cash Flow A |
Cash Flow B |
Cash Flow C |
|
Year 1 |
$1,000 |
$1,000 |
$5,000 |
0.91 |
$ 909 |
$ 909 |
$ 4,545 |
|
Year 2 |
$2,000 |
$1,000 |
$5,000 |
0.83 |
$ 1,653 |
$ 826 |
$ 4,132 |
|
Year 3 |
$3,000 |
$1,000 |
$(5,000) |
0.75 |
$ 2,254 |
$ 751 |
$ (3,757) |
|
Year 4 |
$(4,000) |
$1,000 |
$(5,000) |
0.68 |
$ (2,732) |
$ 683 |
$ (3,415) |
|
Year 5 |
$4,000 |
$3,000 |
$15,000 |
0.62 |
$ 2,484 |
$ 1,863 |
$ 9,314 |
|
Present Value |
$ 4,567.56 |
$ 5,032.63 |
$ 10,819.86 | ||||
Bibliography:
Bekaert, G., & Hodrick, R. (2017). International financial management. Cambridge University Press.
Burtonshaw-Gunn, S. A. (2017). Risk and financial management in construction. Routledge.
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