Question

$10,000 is borrowed, to be repaid in four equal, annual payments with 8% interest. Approximately how much principal is amortized with the first payment?
A. $800

B. $2,219

C. $2,500

D. $3,281

Give me an explanation for the answer, and the written formula to find the answer

Answer 1

• To get to your answer, we must first know what would be the amount of equal annual instalment.
• Equal Annual instalment can be calculated using two methods, as follow:

--#1 Using MS Excel “=pmt()” function, as ‘=pmt(0.08,4,10000)

--#2 By dividing the loan amount by the PVA $1 for 4^th period at 8% discount rate

PVA $1 of 8% 4^th period = 3.312…..

• Equal annual amount = $ 10,000 / 3.312 = $ 3019
• Now, we have calculated what would be the EQUAL Annual payments to be made.

This annual payment would include both ‘principal’ as well as ‘interest’ component.

• The Question asks about how much ‘principal’ is paid when 1^st annual equal payment is made.
• First year interest = 10000 x 8% = $ 800
• First Year Installment = $ 3019
• Hence, principal amount = Total Installment – Interest component

= 3019 – 800 = $ 2,219

• Correct Answer = Option ‘B’ $ 2,219