bmaggie

Which of the following statements about compounding and interest rates is least accurate?

A) Present values and discount rates move in opposite directions.

B) All else equal, the longer the term of a loan, the lower will be the total interest you pay.

C) On monthly compounded loans, the effective annual rate (EAR) will exceed the annual percentage rate (APR).

---

Since the proportion of each payment going toward the principal decreases as the original loan maturity increases, the total dollars interest paid over the life of the loan also increases.

bmaggie

It will cost $20,000 a year for four years when an 8-year old child is ready for college. How much should be invested today if the child will make the first of four annual withdrawals 10-years from today? The expected rate of return is 8%.

A) $66,243.

B) $30,683.

C) $33,138.

---

First, find the present value of the college costs as of the end of year 9. (Remember that the PV of an ordinary annuity is as of time = 0. If the first payment is in year 10, then the present value of the annuity is indexed to the end of year 9). N = 4; I/Y = 8; PMT = 20,000; CPT → PV = $66,242.54. Second, find the present value of this single sum: N = 9; I/Y = 8; FV = 66,242.54; PMT = 0; CPT → PV = 33,137.76.

bmaggie

An investor who requires an annual return of 12% has the choice of receiving one of the following:

1. 10 annual payments of $1,225.00 to begin at the end of one year.
2. 10 annual payments of $1,097.96 beginning immediately.

Which option has the highest present value (PV) and approximately how much greater is it than the other option?

A) Option B's PV is $27 greater than option A's.

B) Option A's PV is $42 greater than option B's.

C) Option B's PV is $114 greater than option A's.

---

Option A: N = 10, PMT = -$1,225, I = 12%, FV = 0, Compute PV = $6,921.52.
Option B: N = 9, PMT = -$1,097.96, I = 12%, FV = 0, Compute PV → $5,850.51 + 1,097.96 = 6,948.17 or put calculator in Begin mode N = 10, PMT = $1,097.96, I = 12%, FV = 0, Compute PV → $6,948.17. Difference between the 2 options = $6,921.52 ? $6,948.17 = -$26.65.

Option B's PV is approximately $27 higher than option A's PV.

bmaggie

John is getting a $25,000 loan, with an 8% annual interest rate to be paid in 48 equal monthly installments. If the first payment is due at the end of the first month, the principal and interest values for the first payment are closest to:

       Principal        Interest

A)  $410.32 $200.00

B)  $443.65   $166.67

C)  $443.65   $200.00

---

Calculate the payment first:

N = 48; I/Y = 8/12 = 0.667; PV = 25,000; FV = 0; CPT PMT = 610.32.

Interest = 0.006667 × 25,000 = $166.67; Principal = 610.32 – 166.67 = $443.65 .

bmaggie

An individual borrows $200,000 to buy a house with a 30-year mortgage requiring payments to be made at the end of each month. The interest rate is 8%, compounded monthly. What is the monthly mortgage payment?

A) $2,142.39.

B) $1,467.53.

C) $1,480.46.

---

With PV = 200,000; N = 30 × 12 = 360; I/Y = 8/12; CPT → PMT = $1,467.53.