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 $20 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 1.5% interest per month.
How much total interest does he expect to earn?

A.) $3.94

B.) $4.35

C.) $3.63

D.) $5.96

Answer 1

Answer:

B. The total interest = $4.35

Explanation:

The first question to answer, is  what is the present value of the annuity of the loan and then based on that the total interest can be calculated.

Present value of annuity= A x [(1-(1+r)-n)/r]*(1+r)

Where the A represents Annuity = or $20

The r represents the rate or 1.5%

and the n represents the number of periods which is 6 months

Calculating the value =

= 20 x [(1-1.015^-6)/0.015]*1.015

= 20 x [(1-0.91454219251)/0.015]*1.015

= 20*5.782644973

=$115.65

Now that the loan amount is known, the Total Interest can be calculated as follows

Total Interest= number of payments x monthly payments) - the loan amount (calculated above)

= 20 x 6 -115.65

= 120-115.65

The total interest = $4.35