Question

. Nonannual compounding period

The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows.

An investor can invest money with a particular bank and earn a stated interest rate of 6.60%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?

Interest Rates
Nominal rate
Periodic rate
Effective annual rate

You want to invest $18,000 and are looking for safe investment options. Your bank is offering you a certificate of deposit that pays a nominal rate of 6% that is compounded monthly. What is the effective rate of return that you will earn from this investment?

6.345%

6.168%

6.046%

6.253%

Suppose you decide to deposit $18,000 in a savings account that pays a nominal rate of 8%, but interest is compounded daily. Based on a 365-day year, how much would you have in the account after nine months? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

$20,068.80

$18,730.88

$19,113.14

$19,495.40

Answer 1

First part:

Nominal interest rate (r) = 6.60%

Given, frequency (t) = quarterly (4 times a year)

Periodic (quarterly) interest rate= Nominal rate/ frequency = 6.60%/4 = 1.65%

Effective annual rate= (1+r/t)^t-1

=(1+6.6%/4)^4-1 = 6.765154%

Second part:

Effective rate of return (EAR)= (1+r)^t-1

Where

r= Nominal interest rate (given as 6%) and

t= frequency (number of times compounded a year, given as monthly or 12)

Plugging the values,

EAR= (1+6%/12)^12-1 = 6.168%

Answer is second choice.

Third part:

Amount in the account after 9 months= P*(1+R/365)^d

Where

P= Principal ($18,000)

R= Nominal interest rate (8%) and

D= period in number of days = (9/12)*365

Amount after 9 months= 18000*(1+8%/365)^(0.75*365)= $19,113.14

Answer is third choice.