Question

You need some money today and the only friend you have that has any is your miserly friend. He agrees to loan you the money you need, if you make payments of $30 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 2 percent interest per month. How much money are you borrowing?a. $164.09b. $168.22c. $169.50d. $170.68e. $171.40

Answer 1

Answer:

The correct option is (b)

Explanation:

Given:

Monthly payment for 6 months = $30 per month

Time period = 6 month (6 periods)

Monthly interest rate = 2%

In order to compute borrowed amount, present value of these payments need to be computed which is an annuity as same amount of $30 is paid.

Checking PVIFA table for 2%, 6 periods, annuity factor is 5.6014.

Borrowed amount = Monthly payment × PVIFA(2%,6)

                            = 30 × 5.6014

                            = $168.042

Borrowed amount is $168.042 or $168.22 approximately (difference in value due to annuity factor being rounded off)