Mikayla wants a new bike.it costs R1750,but her parents said she must buy it herself. She finds out that electronics shop has hire purchase contract at 11.5% interest for 3 years. She will need to pay a 15% deposit. Calculate her monthly instalments over 3 years
The deposit would be 15% of R1750:
R1750 x 0.15 = R262.50
So Mikayla would need to pay R262.50 upfront.
The remaining amount that she needs to finance is:
R1750 - R262.50 = R1487.50
To calculate the monthly instalments, we need to use the formula for compound interest:
A = P*(1 + r/n)^(n*t)
Where:
A = the end amount
P = the initial amount
r = the annual interest rate
n = the number of times interest is compounded per year
t = the time period in years
Mikayla will be paying off her bike over 3 years, so t = 3.
The interest rate is 11.5%, but we need to divide this by the number of times per year that interest is compounded. Let's assume it's compounded monthly, so n = 12.
r = 11.5% / 12 = 0.00958333 (to 8 decimal places)
Now we can plug in the numbers:
A = R1487.50*(1 + 0.00958333/12)^(12*3)
A = R1781.96
So Mikayla will end up paying R1781.96 over 3 years.
To calculate the monthly instalments, we can divide this amount by the number of months over the 3-year period:
R1781.96 / (3*12) = R49.22
So Mikayla's monthly instalments will be R49.22.
To calculate Mikayla's monthly instalments over 3 years with a hire purchase contract at an 11.5% interest rate, we need to determine the principal amount of the loan and the interest payable for each installment.
Step 1: Calculate the deposit amount.
Mikayla needs to pay a 15% deposit on the bike cost, so the deposit amount can be calculated as follows:
Deposit = 15% of R1750
Deposit = (15/100) * R1750
Deposit = R262.50
Step 2: Calculate the principal amount of the loan.
The principal amount is the cost of the bike minus the deposit paid. Therefore:
Principal amount = R1750 - R262.50
Principal amount = R1487.50
Step 3: Calculate the monthly interest rate.
The monthly interest rate can be calculated by dividing the annual interest rate by 12 (number of months in a year).
Monthly interest rate = 11.5% / 12
Monthly interest rate = 0.0958
Step 4: Calculate the monthly installment.
To calculate the monthly installment, we can use the formula for the monthly payment on a loan:
Monthly installment = (Principal amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))
Substituting the values into the formula, we get:
Monthly installment = (R1487.50 * 0.0958) / (1 - (1 + 0.0958)^(-36))
Monthly installment = R68.35 (rounded to 2 decimal places)
Therefore, Mikayla's monthly instalments over 3 years will be approximately R68.35.