Pearson sets up a fund to pay $1000 at the end of each month for 9.5 years. Interest on the fund is 3.9% compounded monthly. (a) How much money must be deposited into the fund? (b) How much will be paid out of the fund? (c) How much interest is earned by the fund?
| a | Present value of annuity= | P* [ [1- (1+r)-n ]/r ] | ||
| P= | Periodic payment | 1,000.00 | ||
| r= | Rate of interest per period | |||
| Annual interest | 3.90% | |||
| Number of payments per year | 12 | |||
| Interest rate per period | 0.039/12= | |||
| Interest rate per period | 0.325% | |||
| n= | number of periods: | |||
| Number of years | 9.5 | |||
| Periods per year | 12 | |||
| number of payments | 114 | |||
| Present value of annuity= | 1000* [ (1- (1+0.00325)^-114)/0.00325 ] | |||
| a | Present value of annuity= | 95,137.25 | ||
| b | Total payments value | 114,000.00 | ||
| c | Interest amount | 18,862.75 |
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