Question

. Will donated $2,000,000 to start a perpetual fund for the purpose of helping people one year after disasters. Will hopes the fund will provide $100,000 each year. Funds are distributed each year, beginning will's donation. If Will can earn 4%, compounded quarterly one over the first 20 years, effective annual raté he must earn over years 21 through forever, is closest to .. a) 50% 5.22% 5.73% d) 6,18% e) 6.39% f) 6.77% g) 6.96% h)712% i) 7.35% k) 8.32% 8. Seven years ago, Bennie took out a loan for the purchase of a home. The loan was for 20 years (monthly payments amount of $300,000 at an interest rate of 4.8%, compounded monthly. Interest rates have dropped, and he is in the pro refinancing the loan over the remaining 13 years at a rate of 4.0%, compounded monthly. To make the refinance wort he should be willing to pay for the refinance charges (at the time of the refinance) is closest to.. a) $10,970 b) $14,082 c) S128,526 7 years a?" e) $8,774 D $11,311 g) $22,534 h) $1,132 i) S9,701 j) $10,532 k) $11,730 ) $9,784 m) $9,107 n) $8,438 o) $8,312 p) $11,218

Answer 1

(7) Present Value of Donations = Initial Donation = $ 2000000 and Annual Donations = $ 100000

The donations earn 4 % per annum compounded quarterly for the first 20 years

Effective Annual Interest Rate for the first 20 years = [1+(4/4)]^(4) -1 = 0.0406 or 4.06%

Let the rate between year 21 and perpetuity be r

Therefore, 2000000 = 100000 x (1/0.0406) x [1-{1/(1.0406)^(20)}] + (100000/r) x [1/(1.0406)^(20)]

2000000 - 1351840.62 = (100000/r) x [1/(1.0406)^(20)]

[648159.38 x (1.0406)^(20)] / 100000 = 1/r

r = 1/14.36674 ~ 0.0696 or 6.96 %

Hence, the correct option is (g)

NOTE: Please raise a separte query for solution to the remaining unelated question as one query is restricted to the solution of only one complete question(with a maximum of four sub-parts)