Question

Your best friend consults you for investment advice. You learn that his tax rate is 30 %​, and he has the following current investments and​ debts:

- A car loan with an outstanding balance of $ 5,000 and a 4.85 % APR​ (monthly compounding)

- Credit cards with an outstanding balance of $ 10,000 and a 14.99 % APR​ (monthly compounding)

- A regular savings account with a $ 30,000 ​balance, paying a 5.51 % effective annual rate​ (EAR)

- A money market savings account with a $ 100,000 ​balance, paying a 5.16 % APR​ (daily compounding)

- A​ tax-deductible home equity loan with an outstanding balance of $ 25,000 and a 4.93 % APR​ (monthly compounding)

a. Which savings account pays a higher​ after-tax interest​ rate?

b. Should your friend use his savings to pay off any of his outstanding​ debts?

Answer 1

Ans a. There are two saving accounts mentioned in the problem

1. Regular Saving Account: Interest rate for the same is mentioned as 5.51% effective annual return. Effective annual return means it has taken compounding into consideration while calculating the interest rate

2. Money Market Savings Account: Interest rate for the same is mentionedas 5.16% APR (Annual Percentage Rate) and daily compounding. Now it has not taken compounding into consideration

To compare both the interest rates we will need to convert APR(Compounding daily) into effective annual return

Steps

1. Divide APR Rate with 365 to get APR daily

5.16% divided by 365 will be 0.014137%

2. Divide percentage figure by 100 to get it into decimal

0.014137% divided by 100 will be 0.00014137

3. For Compounding you need to use the formula ( 1+r)^N -1where r is the daily interest rate in decimal and n is no of days in a year to get the effective annual return. In this particular case ( 1+0.00014137)^365-1 which comes out to be 5.295%

Comparison

Since the effective annual return in normal saving account is higher then the money market saving account, normal saving account will be prefeered. Tax impact will be same on both the accounts.

b) Lets first compare pre tax and post tax interest rates for all the accounts

Type	Ampunt	Rate		Compounding	Effective Annual rate	Post Tax Annual Rate
Car Loan	5000	4.85%	APR	Monthly Compounding	4.965%
Credit Card	10000	14.99%	APR	Monthly Compounding	16.128%
Regular Saving Account	30000	5.51%	EAR	Annual Return	5.51%	3.857%
Money Market Saving Account	100000	5.16%	APR	Daily Compounding	5.295%	3.707%
Home Loan	25000	4.93%	APR	Monthly Compounding	5.049%	3.535%

Now while comparing in the table we can easily identify that our both the saving accounts are giving us lowere return in comparison to what we are paying for Credit card and car loan. While we are getting higher return in both the accounts in comparison to post tax home loan .

We should pay off the credit card & Car loan balance from money market savings account so as to save on the interest cost.