Question

5. (2pts) You are given the following information about an investment account: Date Deposit Balance (before deposit) January 1 10 July 1 X 12 December 31 X Over the year, the time-weighted yield is 0%, and the dollar-weighted yield rate is Y. Find Y.

6. (2pts) You have to get a car loan of $25,000. The bank will finance the car at an annual nominal rate of 12% convertible monthly. If you can afford payments of $500 per month, find the down payment for the car you must make for a 3-year loan. (Down payment = principal – present value of all payments) (Answer: $9946.25) I have the answer to 6 but please show work

Answer 1

Solution 5:

The time weighted yield is calculated using the formula

1 + 0% = 12/10*X/(12 + X)

1 = 12X/(120+10X)

120 + 10X = 12X

2X = 120

X = 60

To find the dollar weighted yield rate, we use the formula

Y = -10/40

Y = -0.25 or -25%

Solution 6:

Given that Principal = $25,000, Annual Nominal rate, i =12%, number of years, n = 3 and Payments, P = $500

First, we calculate the present value of payments

PV of payments = P (PVIFA @ i, n)

PV of payments = $500 (PVIFA @ 12%/12, 3*12) [Since it is compounded monthly, the interest rate is divided by 12 and number of years is multiplied by 12]

PV of payments = $500 (PVIFA @ 1%, 36)

PV of payments = $500 [(1.01^36-1)/(0.01*1.10^36)]

PV of payments = $500 (30.10751)

PV of payments = $15,053.75

Therefore, Down payment = Principal - PV of payments

Down payment = $25,000 - $15,053.75

Down payment = $9,946.25