Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 73.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 73.0 when he fully retires, he will begin to make annual withdrawals of $115,952.00 from his retirement account until he turns 95.00. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 7.00% interest rate.

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 70.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 70.0 when he fully retires, he will begin to make annual withdrawals of $151,219.00 from his retirement account until he turns 85.00. After this final withdrawal, he wants $1.10 million remaining in his account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 9.00% interest rate.

Answer 1

1)

Amount required at 73rd year Px[1-(1=(1+r)^n)]=r Here, 7.00% 22 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% 22 115,952 Amount required at 73rd year 1,282,572.96 115952x(1-(1:(1+7%)^22)):7%

Amount required at 65th year FVX(1=(1+r)^n) Here, 7% 8 1 A Rate per annum B Number of years C Number of compoundings per per annum A:C Rate per period (r) BxC Number of periods (n) Future value (FV) 7% $ 1,282,573 Amount required at 65th year 746,469.14 1282572.96x(1=(1+7%)^8)

Contribution per year for retirement FVA:([(1+r)^n-1)=r) Here, 7% 40 11 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% 40 746,469.14 Contribution per year for retirement $ 3,739.17 746469.14:(((1+7%)^40-1):7%)

2)

$151,219 receipts value at 70th year Px[1-(1=(1+r)^n)]=r| Here, 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) 9.00% 15 1 9.00% 15 151,219 $151,219 receipts value at 70th year 1,218,929.24 151219X(1-(1:(1+9%)^15)):9%

$1,100,000 value at 70th year FVx(1=(1+r)^n) Here, 9% 15 1 A Rate per annum B Number of years C Number of compoundings per per annum A:C Rate per period (r) BxC Number of periods (n) Future value (FV) 9% 15 1,100,000 $1,100,000 value at 70th year 301,991.85 1100000/(1+(1+9%)^15)

Amount required at 65th year FVX(1:(1+r)^n) Here, 9% A Rate per annum B Number of years C Number of compoundings per per annum A:C Rate per period (r) BxC Number of periods (n) Future value (FV) 9% 1,933,853.76 =714924.52+1218929.24 Amount required at 65th year 1,256,872.26 1933853.76x(1=(1+9%)^5)

Contribution per year for retirement FVA: ([(1+r)^n-1]=r) Here, A Interest rate per annum B Number of years C|Number of payments per per annum A: Interest rate per period (r) BxC Number of periods (n) Future value of annuity (FVA) 9% 40 1 9% 40 1,256,872.26 Contribution per year for retirement $ 3,719.85 1256872.26:(((1+9%)^40-1):9%)

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