Question

In: Accounting

Assume you've borrowed 4,000,000 from the bank at 10%. The terms require equal annual installments each...

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.

Solutions

Expert Solution

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


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