Question 1175997: John,a client of UMOJA microfinance institution took a loan of TZS 20000000 on 2 January 2018 which charges 24% interest per annum.using reducing balance method.the loan contract indicated that the loan was supposed to be repaid in 3 months period on loan is to be charged upfront as compulsory saving.required
(a) calculate the total payment (PMT) made each period by the client.
(b) determine the interest which a client is actually paying.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! You've asked this question before, and I provided a detailed solution. Let's reiterate it for clarity.
Given Information:
Loan amount (Principal, P): TZS 20,000,000
Annual interest rate (r): 24% (0.24)
Loan term: 3 months
Interest charged upfront as compulsory savings.
Calculations:
(a) Calculate the total payment (PMT) made each period by the client.
Monthly Interest Rate:
Monthly interest rate (i) = Annual interest rate / 12
i = 0.24 / 12 = 0.02 (or 2%)
Loan Term in Months:
The loan term is 3 months (n = 3).
Upfront Interest (Compulsory Saving):
The interest for the entire loan period is charged upfront.
Total interest = P * i * n = 20,000,000 * 0.02 * 3 = TZS 1,200,000
Effective Loan Amount:
The amount the client effectively receives is the original loan amount minus the upfront interest.
Effective loan amount = 20,000,000 - 1,200,000 = TZS 18,800,000
Monthly Payment (PMT) Using Reducing Balance Method:
We can use the loan payment formula:
PMT = P * [i(1 + i)^n] / [(1 + i)^n - 1]
Where:
PMT = Monthly payment
P = Effective loan amount (TZS 18,800,000)
i = Monthly interest rate (0.02)
n = Number of months (3)
PMT = 18,800,000 * [0.02(1 + 0.02)^3] / [(1 + 0.02)^3 - 1]
PMT = 18,800,000 * [0.02(1.02)^3] / [(1.02)^3 - 1]
PMT = 18,800,000 * [0.02(1.061208)] / [1.061208 - 1]
PMT = 18,800,000 * [0.02122416] / [0.061208]
PMT = 18,800,000 * 0.346757
PMT = 6,518,031.6
Therefore, the monthly payment is approximately TZS 6,518,031.60
(b) Determine the interest which a client is actually paying.
Total Amount Paid:
Total amount paid = Monthly payment * Number of months
Total amount paid = 6,518,031.6 * 3 = TZS 19,554,094.80
Total Interest Paid:
Total interest paid = Total amount paid + Upfront interest - Original loan amount.
Total interest paid = 19,554,094.80 + 1,200,000 - 20,000,000
Total interest paid = 754,094.80
Actual interest rate.
Total interest = 754,094.80
Total amount received = 18,800,000
Percentage of interest = (754,094.80/18,800,000)*100 = 4.01%
4.01% for 3 months.
Annual interest rate = 4.01%*4 = 16.04%
The client is actually paying TZS 754,094.80 in interest on top of the upfront interest, and the actual annual interest rate is 16.04%.
Answers:
(a) Total payment (PMT) made each period: Approximately TZS 6,518,031.60
(b) Interest which a client is actually paying: TZS 754,094.80 and the actual annual interest rate is 16.04%.
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