1. **Problem statement:** Pearson sets up a fund to pay $1000 at the end of each month for 9.5 years. The interest rate is 3.9% compounded monthly. We need to find: (a) The amount of money that must be deposited into the fund now (the present value). (b) The total amount paid out of the fund. (c) The total interest earned by the fund. 2. **Formula used:** This is an annuity problem where payments are made monthly, and interest is compounded monthly. The present value $P$ of an ordinary annuity is given by: $$P = PMT \times \frac{1 - (1 + r)^{-n}}{r}$$ where: - $PMT = 1000$ (monthly payment) - $r = \frac{0.039}{12} = 0.00325$ (monthly interest rate) - $n = 9.5 \times 12 = 114$ (total number of payments) 3. **Calculate the present value:** $$r = 0.039 / 12 = 0.00325$$ $$n = 9.5 \times 12 = 114$$ Calculate $(1 + r)^{-n}$: $$ (1 + 0.00325)^{-114} = 1.00325^{-114} $$ Using a calculator: $$ 1.00325^{-114} \approx 0.698927 $$ Now calculate the numerator: $$ 1 - 0.698927 = 0.301073 $$ Calculate the fraction: $$ \frac{0.301073}{0.00325} = 92.637538 $$ Calculate present value: $$ P = 1000 \times 92.637538 = 92637.538 $$ Rounded to nearest cent: $$ P = 92637.54 $$ 4. **Calculate total amount paid out:** Total payments = $PMT \times n = 1000 \times 114 = 114000$ 5. **Calculate interest earned:** Interest = Total paid out - Present value deposited $$ = 114000 - 92637.54 = 21362.46 $$ **Final answers:** (a) $92637.54$ (b) $114000$ (c) $21362.46$