Question

using formula OR Excel function.

For questions 1 - 4 use a required nominal annual return:			5.00%
1. Consider a 1-year CD.		Principal value	$5,000.00
What is the future value of the CD in 1 year AND what is the effective annual rate?
		Future Value	EFF
a. annual compounding?
b. semi-annual compounding?
c. quarterly compounding?
d. monthly compounding?
e. daily compounding?
2. Rework problem #1 assuming a 5-year CD with $5000 principal.
		Future Value	EFF
a. annual compounding?
b. semi-annual compounding?
c. quarterly compounding?
d. monthly compounding?
e. daily compounding?

Answer 1

It seems that in the question 1 principal amount is missing thus we will solve it considering no principal thus you can just multiply the principal amount to the interest rates to get the amount

Nominal interest rate = 5%

1. annual compounding

As we know that by logic if any amount is just compounded yearly at any rate the effective rate is same as the nominal interest rate.

Now we are given nominal interest of 5% thus effective interest rate with yearly compunding would be 5%. We will also do it by the formula to make you understand the concept of compounding.

APR or effective interest rate is given by (1+ r/i)^i - 1

Here r is the nominal interest rate

i = no of times the amount is compounded in a single period (Here single period is a year)

Thus effective rate for annual compounding is = (1+0.05/1)^1 -1 = 0.05 = 5%

For principal for e.g. $5000

Effective return at 5% would be 5000 + 5000 * 0.05 = 5250

( You can also do 5000 * 1.05 = 5250)

2. Semi annual compounding

Now in this the amount is compounded semi annually

so r = 0.05 or 5%

i = 2

Thus effective rate for semi-annual compounding is = (1+0.05/2)^2 -1

= (1.025)^2 -1

= 0.050625

= 5.0625%

For principal $5000

Effective return at 5.0625% would be 5000 + 5000 * 0.050625 = 5253.125

( You can also do 5000 * 1.050625 = 5253.125)

3. Quarterly Compounding

Now in this the amount is compounded quarterly

so r = 0.05 or 5%

i = 4

Thus effective rate for semi-annual compounding is = (1+0.05/4)^4 -1

= (1.0125)^4 -1

= 1.0509453369 -1

0.050945 = 5.0945%

For principal $5000

Effective return at 5.0945% would be 5000 + 5000 * 0.050945 = 5254.725

( You can also do 5000 * 1.050945 = 5254.725)

4. monthly compounding

Now in this the amount is compounded monthly

so r = 0.05 or 5%

i = 12

Thus effective rate for semi-annual compounding is = (1+0.05/12)^12 -1

= (1.0041666667)^12 -1

= 1.0511618979 -1

= 0.0511618979

= 5.12%

For principal $5000

Effective return at 5.12% would be 5000 + 5000 * .0512 = 5256

( You can also do 5000 * 1.0512 = 5256)

e. Daily Compounding

Now in this the amount is compounded monthly

so r = 0.05 or 5%

i = 365

Thus effective rate for semi-annual compounding is = (1+0.05/365)^365 -1

= (1.0001369863)^365 -1

= 1.0512674965 - 1

= 0.0512674965

= 5.13%

For principal $5000

Effective return at 5.13% would be 5000 + 5000 * .0513 = 5256.5

( You can also do 5000 * 1.0513 = 5256.5)