Question

A couple will retire in 40 years; they plan to spend about $21,000 a year in retirement, which should last about 20 years. They believe that they can earn 7% interest on retirement savings.

a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

(I got 1,114.40 which it says is correct)

b. How would the answer to part (a) change if the couple also realize that in 15 years they will need to spend $51,000 on their child’s college education? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

(i got 2,029.53, which it says is incorrect)

Answer 1

a)

Amount required for retirement income Px[1-(1=(1+r)^n)]=r Here, 7.00% 20 A Interest rate per annum B Number of years C Number of compoundings per per annum A:C Interest rate per period (r) BxC Number of periods (n) Payment per period (P) 7.00% 20 21,000 Amount required for retirement income $ 222,474.30 21000x(1-(1-(1+7%)^20)): 7%

Contribution per year for retirement FVA: ([(1+r)^n-1]=r) Here, 7% 40 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) 7% 40 222,474.30 Contribution per year for retirement $ 1,114.40 222474.3=(((1+7%)^40-1):7%)

b)

Contribution per year for retirement FVA:([(1+r)^n-1)=r) Here, 7% 40 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) 7% 40 499,273.36 =222474.3+51000*(1+7%)^25 Contribution per year for retirement $ 2,500.93 499273.36:(((1+7%)^40-1):7%)

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