Your company must make payments of $100,000 each year for 10 years,with the first payment to be made 10 years from today.To prepare for these payments,your company must make 10 equal annual deposits into an account which pays a simple interest rate of 7 percent,daily compounding (360-day year).Funds will remain in the account during both the accumulation period (the first 10 years)and the distribution period (the last 10 years),and the same interest rate will be earned throughout the entire 20 years.The first deposit will be made immediately.How large must each deposit be?
A) $47,821.11
B) $49,661.86
C) $51,234.67
D) $52,497.33
E) $53,262.39

Question

Quizplus · Accepted Answer

To find the size of each deposit, we need to use the formula for the present value of an annuity:

PV = Pmt x ((1 - (1 + i)^(-n)) / i)

where PV is the present value of the payments, Pmt is the amount of each payment, i is the interest rate per period, and n is the number of periods.

We know that PV = 10 x $100,000 = $1,000,000, i = 7% / 360 = 0.0194 per day, and n = 10 x 360 = 3,600 days. We can solve for Pmt:

Pmt = PV / ((1 - (1 + i)^(-n)) / i) = $1,000,000 / ((1 - (1 + 0.0194)^(-3600)) / 0.0194) = $49,661.86 (rounded)

Therefore, the company must make annual deposits of $49,661.86 to accumulate $1,000,000 in 10 years, in order to be able to make payments of $100,000 each year for 10 years after that. The best choice is B.

Your Company Must Make Payments of $100,000 Each Year for 10