Question #148964

Mr. Rahul has been saving Rs.9,500 at the beginning of every quarter for 25 years at an average return of 14% p.a. compounded quarterly. He has to set apart Rs.15,00,000 for his daughter’s marriage and Rs.10,00,000 for his son’s marriage from accumulated sum after 25 years. He is saving separately for their education and he wishes to withdraw a certain amount for the next 25 years on the remaining sum. The money accumulated will

be invested at a rate of 8% p.a. How much can he withdraw at the beginning of every year?

Expert's answer

In this case, first we calculate the accumulated sum that Mr. Rahul has been saving.

We are told that he has been saving Rs.9,500 at the beginning of every quarter at the an annual rate of "14\\%" compounded quarterly, there are 4 quarters in a year ,so we will divide the average rate by 4 to get the quarterly compounded rate and multiply the number of years by 4 to get the number of periods that the transaction took place.

Note the payments are made at the beginning of each quarter, this means that it is an annuity due.

To get the accumulated amount after 25 years ,we will calculate the (Future Value) of the savings he has been making.

Savings(Pmt) = Rs.9,500

Average return(r) = "\\frac{14\\%}{4}=3.5\\%=0.035"

Number of periods(n) = "25\\times 4 = 100"

Future Value annuity due = "Pmt \\times [\\frac{((1+r)n-1)}{r}]\\times (1+r)"

"=9500\\times [\\frac{((1+0.035)100-1)}{0.035}]\\times (1+0.035)=9500\\times 862.6116567\\times1.035=Rs. 8481629.114"

Accumulated amount after 25 years = Rs.84,81,629.11

We are told that he has to set aside Rs.15,00,000 for his daughter's marriage and Rs.10,00,000 for his son's marriage from the accumulated amount.

To get the amount remaining after setting aside amount for his daughter's and son's marriage=

"Rs.8481629.11-Rs.1500000-Rs.1000000=Rs. 5981629.11"

He wishes to withdraw a certain amount(Pmt)on the remaining amount for 25 years

Remaining amount(Present Value now) = "Rs.8481629.11-Rs.1500000-Rs.1000000=Rs. 5981629.11"

Investment rate(r)= "8\\%P.a= 0.08"

Number of periods(n) = 25 years

Amount to be withdrawn at the beginning of each year(Pmt) = ? note this is an annuity due as transaction takes place at the beginning of the period

We already have the present value of the annuity due, so we calculate the Pmt using the formula below.

Present Value of an annuity due "=Pmt \\times [\\frac{(1-(1+r)-n)}{r}]"

"Rs.5981629.11=Pmt\\times [\\frac{(1-(1+0.08)-25)}{0.08}]\\times (1+0.08)"

"=Pmt \\times 10.67477619\\times 1.08=11.52875828Pmt"

"Pmt = \\frac{Rs.5981629.11}{11.52875828}=Rs. 518844.1776"

Amount to be withdrawn at the beginning of every year "=Rs. 518844.18"

Learn more about our help with Assignments: Finance

## Comments

## Leave a comment