Question

If you need $5,000 in four years from today and you can make quarterly deposits of $370 in your money market account, what is the APR you are looking for?

If you need $5,000 in four years from today and you can make quarterly deposits of $370 in your money market account, what is the APR you are looking for?

You will make the following investments for a boat: $2,500 today, $3,000 at the end of year three, and $1800 at the end of year five. How much will you have in five years if you can earn 3.2% on your investments?

You have two opportunities for investments. Bank Celtics will offer you 5.4% with daily compounding while Bank Hawks will offer you 5.44% with monthly compounding. What are the relevant interest rate comparisons for decision making?

Answer 1

1]

Quarterly deposit = $370

There are 4 quarters per year.

If quarterly deposits are made for 4 years, amount in account at end of 4 years = $370 * 4 * 4 = $5,920

Hence, with zero APR (0% APR), the account will have more than $5,000 (to be precise, $5,920) at the end of 4 years with quarterly deposits

2]

future value = present value * (1 + r)ⁿ

where r = interest rate

n = number of years

Amount you will have in 5 years = ($2,500 * (1 + 3.2%)⁵) + ($3,000 * (1 + 3.2%)²) + ($1,800 * (1 + 3.2%)⁰​​​​​​​)

Amount you will have in 5 years = 7,921.50

3]

Effective annual rate (EAR) = (1 + (APR/n))ⁿ - 1

where n = number of compounding periods per year

Celtics Bank EAR = (1 + (5.4%/365))³⁶⁵ - 1

Celtics Bank EAR = 5.5480%

Hawks Bank EAR = (1 + (5.44%/12))¹² - 1

Hawks Bank EAR = 5.5777%

Hawks Bank should be chosen as it has a higher EAR