Question

A Mother wants Rs 300,000 after 3 years from now & Rs 500,000 after five years from now separately. If the interest rate is 12% compounded quarterly, what would be the amount of instalment to be deposited by her at the start of 1st, 8th, and 13th quarter?

Answer 1

To calculate the amount of each installment to be deposited by the mother, we can use the formula for calculating the maturity value of a loan with compound interest.

Step-by-step explanation:

To calculate the amount of each installment to be deposited by the mother, we can use the formula for calculating the maturity value of a loan with compound interest: MV = PV(1+r/n)^(nt)

Where:

• MV is the maturity value
• PV is the principal amount (amount to be deposited)
• r is the annual interest rate (12%, which is converted to 0.12)
• n is the number of times interest is compounded per year (quarterly, so 4)
• t is the number of years (3 for the first question, 5 for the second question)

For the first question, plugging in the values:

MV = 300,000(1+0.12/4)^(4*3)

MV = 300,000(1.03)^12

MV ≈ 447,437.27

To find the amount of each installment, we can rearrange the formula:

PV = MV/(1+(r/n))^(nt)

PV = 447,437.27/(1+(0.12/4))^(4*3)

PV ≈ 265,714.29

So, at the start of the 1st quarter, the mother should deposit approximately Rs 265,714.29 as an installment.