Question

A problem is listed below. Identify its type.

Julie's parents' 25th anniversary is in 2 years. She'd like to give her parents a vacation package for their anniversary. She anticipates the vacation package will cost her $2000. An account at her bank pays 5% per year compounded monthly. How much does she need to deposit today in this account, so that she can buy the package deal for her parents' anniversary?
a) Simple Interest
b) Future Value with compound interest
c) Future Value with simple interest
d) Effective Rate
e) Present Value with compound interest

Answer 1

e) Present Value with compound interest

Explanation:

in order to determine how much money does Julie need to deposit we have to use the present value formula with compound interest:

present value = future value / (1 + i/12)ⁿ

• future value = $2,000
• i/12 = 5%/12 = 0.4167%
• n = 24

$2,000 = present value x (1 + 0.4167%)²⁴

present value = $2,000 / (1 + 0.4167%)ⁿ = $1,810.05

you can also calculate it using the future value formula, but you will end with the present value formula:

future value = present value x (1 + i/12)ⁿ

present value = future value / (1 + i/12)ⁿ ⇒ you are adding 1 more step

you could also calculate it using the present value formula and the effective annual rate:

effective rate = (1 + 0.05/12)¹² - 1 = 5.1162%

present value = $2,000 / (1 + 5.1162)² = $1,810.05 ⇒ but again you are just adding more steps into the process