Question

6. Actively managed mutual funds charge higher management fees than passive funds. Assume that the net return to an active fund (after fees) is 7.32 percent (0.61 percent per month) and the net return to a passive fund is 8.25 percent (0.6875 percent per month). Consider an investor who invests $675 per month (end-of-month) over twenty years in the passive fund. Now consider an investor who invests on a monthly basis over twenty years in the active fund. If the active fund investor wants the same future value as the passive fund investor, then how much more must she invest per month?
A. more than $81.25
B. less than $81.25 but more than $70.50
C. less than $70.50 but more than $62.25
D. less than $62.25 but more than $53.80
E. less than $53.80

7. Hardy Hammers, Inc. is planning to borrow $1,175,000 on a 10-year, 6.75 percent, annual payment, fully amortized term loan. How much of the payment made at the end of the third year will represent interest paid?
A. less than $61,240
B. more than $61,240 but less than $63,285
C. more than $63,285 but less than $65,330
D. more than $65,330 but less than $67,375
E. more than $67,375

8. Hardy Hammers, Inc. is planning to borrow $1,175,000 on a 10-year, 6.72 percent, annual payment, fully amortized term loan. How much of the payment made at the end of the ninth year will represent repayment of principal?
A. less than $136,875
B. more than $136,875 but less than $139,370
C. more than $139,370 but less than $142,145
D. more than $142,145 but

Answer 1

Q - 6

The correct answer is option A. more than $81.25

i_a = interest rate per month on active fund = 0.61%

i_p = interest rate per month on passive fund = 0.6875%

n = 20 years = 12 x 20 = 240 months

A_p = Annuity in passive funds = $ 675

A_a = Annuity in active fund

FV_{passive fund} = A_p / i_p x [(1 + i_p)ⁿ - 1] = 675 / 0.6875% x [(1 + 0.6875%)²⁴⁰ - 1] = $  410,171

This should be the FV of active fund also and hence following equation should hold true:

FV_{active fund} = A_a / i_a x [(1 + i_a)ⁿ - 1] = A_a / 0.61% x [(1 + 0.61%)²⁴⁰ - 1] = 541.645A_a = $  410,171

Hence, A_a = 410,171 / 541.645 = $ 757.27

Hence, A_a - A_p = 757.27 - 675 = $ 82.27

Hence, the correct answer is option A. more than $81.25

Q - 7

This can be calculated using the IPMT function of excel.

Interest portion in the 3rd payment = IPMT(Rate, Period, Total period, PV) = IPMT(6.75%, 3, 10, -1175000) = $67,303.26

Hence, the correct answer is option D. more than $65,330 but less than $67,375

Q - 8

This can be calculated using the PPMT function of excel.

Principal portion in the 9th payment = PPMT(Rate, Period, Total period, PV) = IPMT(6.72%, 9, 10, -1175000) = $144,993.04

The listed options are not complete. Option D is written partly and option E has gone missing while you have pasted the question. Your answer can be option D (which is incomplete) or E. Please check it at your end and choose the correct option.