Graham receives $640,000 at his retirement. he invests x in a twenty-year annuityimmediate with annual payments and the remaining $640, 000 - x is used to purchase a perpetuity-immediate with annual payments. his total annual payments received during the first twenty years are twice as large as those received thereafter. the annual effective interest rate is 5%. find x.

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Nelson Buck

7 April, 15:12

Graham receives $640,000 at his retirement. he invests x in a twenty-year annuityimmediate with annual payments and the remaining $640, 000 - x is used to purchase a perpetuity-immediate with annual payments. his total annual payments received during the first twenty years are twice as large as those received thereafter. the annual effective interest rate is 5%. find x.

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Will Holloway · Answer 1

For the amount invested in the 20 year annuity immediate,

the return will be;

r / (1 - (1+r) ^-n) = 0.05 / (1 - 1.05^-20)

= 0.0802425872

= 8.02425872%

Now, return on perpetuity-immediate = 5%

So, 5% + 8.02425872% = 13.02425872

for equal returns from both investments,

X = 5 / (13.02425872) x 640,000

= $245,695.365

= $ 245,695.36