Question

You are looking to take out a ​$47，000 loan to pay for school. The loan would be a​ five-year loan. The lender offers you a 7​% interest rate on the loan and also offers to structure it in one of three​ ways:

what‘s your ending balance of the first year?
​a) As a discount loan
​b) As an​ interest-only loan

c) As an amortized loan.

Answer 1

1. Discount loan are the loan which are given after deducting the interest amount from loan amount. And Interest is calculated on total loan amount. In the absence of information, We are considering it that it is simple interest dicount loan.

Discount = 47000*7%*5 = 47000*0.07*5 = 16450

So, Loan given amount = 47000-16450 = $30,550

So, ending balance 1st year = 30550 + Interest of 1 year = 30550 + 16450/5 = $33,840

2.

Interest only loan are those in which only interest payment will be done every year and principal payment will made at the end of Loan period.

So,

Ending balance of 1st year will be $ 47,000 if the interest has been paid on last date of year. or

Ending balance of 1st year will be $ 50,290 (47,000 + 3290) if the interest will be paid on first day of next year.

3.

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

Where, (1+r)-ⁿ = 1/(1+r)ⁿ

           n = 5

           r = 0.07

           P = ??

47000 = P * [1-(1+0.07)^-5]/0.07

47000 = P * [1-(1.07)^-5]/0.07

47000 = P * [1-0.712986]/0.07

47000 = P* 4.10019

P = $ 11,462.86

So, Ending Balance of 1st year after 1st installment = 47000*(1.07) - 11462.86

                                                                                   = 50290 - 11462.86

                                                                                   = $ 38,827.14