Question

You wish to retire in 20 years, at which time you want to have accumulated enough money to receive an annual annuity of $24,000 for 25 years after retirement. During the period before retirement you can earn 10 percent annually, while after retirement you can earn 12 percent on your money. What annual contributions to the retirement fund will allow you to receive the $24,000 annuity

Answer 1

$3,286.52

Step-by-step explanation:

Interest rate per annum = 12.00%

Number of years = 25

Number of compounding per per annum = 1

Interest rate per period (r) = 12.00%

Number of periods (n) = 25

Payment per period (P) = $24,000

PV of $24,000 payments after 20 years = P * [1 - (1/(1+r)^n)]/ r

PV of $24,000 payments after 20 years = 24000*[1-(1/(1+12%)^25]/12%

PV of $24,000 payments after 20 years = $188,235.34

Interest rate per annum = 10.00%

Number of years= 20

Number of payments per per annum = 1

Interest rate per period (r) = 10.00%

Number of periods (n) = 20

Future value of annuity (FVA) = $188,235

Annual contribution (P) = FVA/ ([ (1+r)^n - 1] / r)

Annual contribution (P) = 188235/(((1+10%)^20-1)/10%)

Annual contribution (P) = $3,286.52