Question

# a man wishes to save for his retirement pension plan which is 36 years from now....

a man wishes to save for his retirement pension plan which is 36 years from now. he planned to receive 100000 at the end of each year for the nest 15 years starting from the first year of his retirement. if the insurance company offers an investment of 11.495% interest rate compounded quarterly, what will be hi s quarterly payments.

Solve quickly I get you UPVOTE directly
Thank's
Abdul-Rahim Taysir

Step - 1:

first we have to calculate present value of retirement benefits (i.e., present value of 100,000 payments at the starting of retirement year)

EAR = (1 + (r/n))^n - 1

where,

r = rate of interest per annum

n = number of compounding periods

EAR = (1 + (11.495%/4))^4 - 1 = 12%

Present value of annuity = P*[1 - (1+r)^-n / r ]

where , P = annual payments

r = effective annual rate

n = number of periods

Present value = 100000*[1 - (1+12%)^-15 / 12% ]

= 681,086.45

Future value of annuity = P*[(1+r)^n - 1 / r ]

we want \$681,086.54 at the end of 36 years i.e., 36*4 = 144 periods

interest rate per quarter = 11.495% / 4 = 2.874%

681,086.45 = P*[(1+2.874%)^144 - 1 / 2.874% ]

P = 681,086.45 / 2023.03

Quarterly payments = \$336.67

(NOTE :it is assumed that payments occur at the end of each quarter (ordinary annuity))

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