Question

1. A bank pays a quoted annual (simple) interest rate of 8 percent. However, it pays interest (compounds) on a daily basis using a 365-day year. What is the effective annual rate of return? Show details of the EAR formula.

2. You have just taken out a 30-year mortgage on your new home for $120,000. This mortgage is to be repaid in 360 equal monthly installments. If the stated (simple) annual interest rate is 14.75 percent, what is the amount of each of the monthly installments? Indicate where your answer is below.

N =

I/Y =

PV =

PMT =

FV =

Answer 1

Answer to Question 1:

Annual interest rate = 8.00%

Daily interest rate = Annual interest rate / 365
Daily interest rate = 8.00% / 365
Daily interest rate = 0.02192%

Effective annual rate = (1 + Daily interest rate)^365 - 1
Effective annual rate = (1 + 0.0002192)^365 - 1
Effective annual rate = 1.0833 - 1
Effective annual rate = 0.0833 or 8.33%

Answer to Question 2:

Amount borrowed = $120,000

Annual interest rate = 14.75%

Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 14.75% / 12
Monthly interest rate = 1.22917%

Time period = 30 years or 360 months

Using financial calculator:
I = 0.0122917
N = 360
PV = -120000
FV = 0

PMT = 1493.37

Monthly payment = $1,493.37