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Homework answers / question archive / Determine the current amount of money that must be invested at 6% nominal interest, compounded monthly, to provide an annuity of $15,000 (per year) for 5 years, starting 9 years from now
Determine the current amount of money that must be invested at 6% nominal interest, compounded monthly, to provide an annuity of $15,000 (per year) for 5 years, starting 9 years from now. The interest rate remains constant over the entire period of time.
Step 1 Caluculation of Effective rate of Interest
| EAR = [ ( 1 + r ) ^ n ] - 1 | |
| = [ ( 1 + 0.005 ) ^ 12 ] - 1 | |
| = [ ( 1.005 ) ^ 12 ] - 1 | |
| = [ 1.0617 ] - 1 | |
| = 0.0617 | |
| I.e EAR is 6.17 % |
Step 2: Calculation of FV of Annutiy
| PV of Annuity | |
| Particulars | Amount |
| Cash Flow | $ 15,000.00 |
| Int Rate | 6.1700% |
| Periods | 5 |
| PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r | ||
| = $ 15000 * [ 1 - [(1+0.0617)^-5]] /0.0617 | ||
| = $ 15000 * [ 1 - [(1.0617)^-5]] /0.0617 | ||
| = $ 15000 * [ 1 - [0.7413]] /0.0617 | ||
| = $ 15000 * [0.2587]] /0.0617 | ||
| = $ 62894.31 |
Step 3: Caluculation annutity Value today
| Particulars | Amount |
| Future Value | $ 62,894.00 |
| Int Rate | 6.170% |
| Periods | 8 |
| Present Value = Future Value / ( 1 + r )^n | |
| = $ 62894 / ( 1 + 0.0617 ) ^ 8 | |
| = $ 62894 / ( 1.0617 ) ^ 8 | |
| = $ 62894 / 1.6144 | |
| = $ 38957.82 | |
| Present Value: |
| PV = FV / (1+r)^n |
| Where r is Int rate per period |
| n - No. of periods |
