In: Accounting
Assume you've borrowed 4,000,000 from the bank at 10%. The terms require equal annual installments each year for 5 years. What is the amount of those installments?
Assume the same facts as the previous question, except assume 10 semi-annual installments. What would be the amount of those installments? Please round your answer to the nearest whole dollar.
Answer)
Part -1 (Installments are to be paid annually)
Amount Borrowed |
$1,000,000 |
Rate of interest |
10% |
Repayment interval |
Annually |
Number of Periods |
5 years |
Calculation of amount of installments:
Amount of installment = a/ [{(1 + r) ^ n} – 1]/ [r (1 + r) ^ n]
Where,
a = amount borrowed,
r = effective annual rate of return
n = number of periods
Amount of installment = $ 4,000,000/ [{(1 + .10) ^ 5} – 1]/ [0.10 (1 + 0.10) ^5]
= $ 4,000,000/ [1.61051 -1]/ 0.161051
= $ 4,000,000/3.79079
= $1,055,189 (Approximately)
Therefore the amount of annual installment will be $ 1,055,189.
Part -2 (Installments are to be paid semi-annually)
Amount Borrowed |
$1,000,000 |
Rate of interest |
10% |
Repayment interval |
Semi-Annually |
Number of Periods |
10 semi-annual periods |
Calculation of amount of installments:
Amount of installment = a/ [{(1 + r) ^ n} – 1]/ [r (1 + r) ^ n]
Where,
a = amount borrowed,
r = effective annual rate of return
n = number of periods
Amount of installment = $ 4,000,000/ [{(1 + .05) ^ 10} – 1]/ [0.05 (1 + 0.05) ^10]
= $ 4,000,000/ [1.62889463 -1]/ 0.08144473
= $ 4,000,000/7.721735
= $518,018 (Approximately)
Therefore the amount of semi- annual installment will be $ 518,018