Question

A company wants to buy a piece of land valued at N 15 000 000. The company agrees an amortization loan of 12% per annum over 30 years. a) what monthly repayment must the company make ? b) how much altogether does it cost the company to pay off the amortization loan?​

Answer 1

approximately N 48,849,418.40 to pay off the amortization loan altogether.

Explanation:

Where: M = Monthly payment

P = Principal loan amount

r = Monthly interest rate

n = Total number of payments (in months)

In this case, the principal loan amount (P) is N 15,000,000, the annual interest rate is 12% (or 0.12 as a decimal), and the loan term is 30 years (or 360 months).
a) To find the monthly repayment, we need to calculate the monthly interest rate (r) and the total number of payments (n):

Monthly interest rate (r) = Annual interest rate / 12 r = 0.12 / 12 = 0.01

Total number of payments (n) = Loan term in years * 12 n = 30 * 12 = 360

Now we can plug these values into the formula:

M = 15,000,000 * 0.01 * (1 + 0.01)^360 / ((1 + 0.01)^360 - 1)

Using a calculator, we can find that the monthly repayment (M) is approximately N 136,033.94.
b) To calculate the total cost of the amortization loan, we can multiply the monthly repayment by the total number of payments:

Total cost = Monthly repayment * Total number of payments Total cost = 136,033.94 * 360

Using a calculator, we can find that the total cost of the amortization loan is approximately N 48,849,418.40.

So, the company must make a monthly repayment of approximately N 136,033.94, and it will cost the company approximately N 48,849,418.40 to pay off the amortization loan altogether.

Answer 2

The monthly repayment the company must make on the loan is N 161,451.97.

The total cost to pay off the amortization loan over 30 years is N 58,122,708.20.

To calculate the monthly repayment a company must make on an amortization loan of N 15,000,000 with a 12% per annum interest rate over 30 years, we use the formula:

PMT = P × [i(1 + i)^n] / [(1 + i)^n − 1]

Where:

PMT is the monthly paymentP is the principal loan amount i is the monthly interest raten is the number of payments (months)

The monthly interest rate is the annual rate divided by 12. So, i = 12% / 12 = 1%. Hence, i = 0.01 in decimal form.

The total number of payments for a 30-year loan is 30 × 12 = 360 months.

Substituting these values into the formula gives us:

PMT = 15,000,000 × [0.01(1 + 0.01)^360] / [(1 + 0.01)^360 − 1]

Performing the calculation:

PMT = 15,000,000 × [0.01(1 + 0.01)^360] / [(1 + 0.01)^360 − 1] = N 161,451.97

So the monthly repayment the company must make is N 161,451.97.

To calculate the total cost of the amortization loan, multiply the monthly payment by the number of payments:

Total Cost = PMT × n

Total Cost = N 161,451.97 × 360 = N 58,122,708.20

The total cost for the company to pay off the amortization loan is N 58,122,708.20.