Mr. Asti earns UGX 1.5 million per month. He intends to buy a house but his current savings are UGX 10 million. A real estate company is selling Mr. Droti's dream home at UGX50 million. A bank which offers a loan at a compound interest rate of 9% per annum, after a down payment of UGX 10 million is willing to give Mr. Droti a loan so that he pays back in installments for 5 years.
a) How much money will Droti pay for each installment?
b) Write down the formula for computing the monthly payments.

Question

Mr. Asti earns UGX 1.5 million per month. He intends to buy a house but his current savings are UGX 10 million. A real estate company is selling Mr. Droti's dream home at UGX50 million. A bank which offers a loan at a compound interest rate of 9% per annum, after a down payment of UGX 10 million is willing to give Mr. Droti a loan so that he pays back in installments for 5 years. 
a) How much money will Droti pay for each installment? 
b) Write down the formula for computing the monthly payments.

GinnyAnswer · Answer

Calculate the loan amount by subtracting the down payment from the house price: 50 , 000 , 000 − 10 , 000 , 000 = 40 , 000 , 000 . 
 Determine the monthly interest rate by dividing the annual interest rate by 12: 0.09/12 = 0.0075 . 
 Calculate the number of monthly payments by multiplying the loan repayment period in years by 12: 5 ∗ 12 = 60 . 
 Compute the monthly installment amount using the loan amortization formula: M = 40 , 000 , 000 ∗ 1 − ( 1 + 0.0075 ) − 60 0.0075 ​ = 830334.21 . The formula for monthly payments is M = P ∗ 1 − ( 1 + i ) − n i ​ . 
 
 Explanation 
 
 Understanding the Problem Mr. Asti wants to buy a house for UGX 50 million but only has UGX 10 million in savings. He needs a loan for the remaining amount. A bank offers him a loan at a 9% annual compound interest rate, which he will repay over 5 years in monthly installments. We need to calculate the amount of each installment and provide the formula for calculating monthly payments. 
 
 Calculating the Loan Amount First, we need to determine the loan amount. This is the price of the house minus Mr. Asti's current savings (down payment). L o an A m o u n t = Ho u se P r i ce − Do w n P a y m e n t L o an A m o u n t = 50 , 000 , 000 − 10 , 000 , 000 = 40 , 000 , 000 The loan amount is UGX 40,000,000. 
 
 Determining the Monthly Interest Rate Next, we need to convert the annual interest rate to a monthly interest rate. Since the interest is compounded annually but payments are made monthly, we divide the annual rate by 12. M o n t h l y I n t eres tR a t e = A nn u a l I n t eres tR a t e /12 M o n t h l y I n t eres tR a t e = 9%/12 = 0.09/12 = 0.0075 The monthly interest rate is 0.0075 or 0.75%. 
 
 Calculating the Number of Monthly Payments Now, we calculate the total number of monthly payments. Since the loan is repaid over 5 years, we multiply the number of years by 12. N u mb ero f M o n t h l y P a y m e n t s = L o an R e p a y m e n tP er i o d ( in ye a rs ) ∗ 12 N u mb ero f M o n t h l y P a y m e n t s = 5 ∗ 12 = 60 There will be 60 monthly payments. 
 
 Calculating the Monthly Installment Amount We use the loan amortization formula to calculate the monthly installment amount: M = P ∗ 1 − ( 1 + i ) − n i ​ Where:

M = Monthly payment 
 P = Loan amount (UGX 40,000,000) 
 i = Monthly interest rate (0.0075) 
 n = Number of months (60) 
 
 Plugging in the values: M = 40 , 000 , 000 ∗ 1 − ( 1 + 0.0075 ) − 60 0.0075 ​ M = 40 , 000 , 000 ∗ 1 − ( 1.0075 ) − 60 0.0075 ​ M = 40 , 000 , 000 ∗ 1 − 0.6386996985927701 0.0075 ​ M = 40 , 000 , 000 ∗ 0.3613003014072299 0.0075 ​ M = 300 , 000/0.3613003014072299 M = 830334.21 Therefore, Mr. Asti will pay approximately UGX 830,334.21 for each installment. 
 
 Stating the Formula for Monthly Payments The formula for computing the monthly payments is: M = P ∗ 1 − ( 1 + i ) − n i ​ Where:

M = Monthly payment 
 P = Loan amount 
 i = Monthly interest rate 
 n = Number of months

Final Answer Mr. Asti will pay approximately UGX 830,334.21 for each installment. The formula for computing the monthly payments is: M = P ∗ 1 − ( 1 + i ) − n i ​ Where:

M = Monthly payment 
 P = Loan amount 
 i = Monthly interest rate 
 n = Number of months 
 
 Examples 
 Understanding loan installments is crucial in personal finance. For instance, when buying a car, a similar calculation helps determine the monthly payments. Suppose you take a loan of $20,000 at an annual interest rate of 6% to be repaid over 4 years. Using the same formula, you can calculate your monthly payments, allowing you to budget effectively and understand the total cost of the car over the loan period. This ensures you make informed financial decisions and avoid unexpected costs.

Answer (1)

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