Question

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A couple is planning to finance its three-year-old son's university education. Money can be deposited at 5% compounded quarterly. What quarterly deposit must be made from the son's 3rd birthday to his 18th birthday to provide $8000 on each birthday from the 18th to the 21st? (Note that the first deposit is made three months after the 3rd birthday and the last deposit is made on the date of the first withdrawal.) Answer:

Answer 1

Required balance in savings a/c P+Px[1-(1:(1+r)^(n-1)]=r Here, 5.09% =(1+5%/4)^4-1 4 1 Interest rate per annum 2 Number of years 3 Number of compoundings per per annum = 1:3 Interest rate per period (r) = 2x3 Number of periods (n) Payment per period (P) 5.09% 8,000 Required balance in savings a/c 29,747.45 8000+8000x(1-(1+5.09%))^(4-1)=5.09%

Deposit in each quarter (P) FVA:([(1+r)^n-1]=r) Here, A Interest rate per annum B Number of years C Number of payments per per annum A:C Interest rate per period (r) BxC Number of periods (n) Future value of annuity (FVA) 5% 15 4 1.25% 29,747.45 Deposit in each quarter (P) $ 335.85 29747.45:(((1+1.25%)^60-1):1.25%)

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