Answer to Question #138154 in Finance for CH Tan

Question #138154
A man is planning to retire in 25 years. He wishes to deposit a regular amount every three
months until he retires, so that, beginning of one year following his retirement, he will
receive annual payments of $60,000 for the next 10 years. How much must he deposit if
the interest rate is 6 percent compounded quarterly?
1
Expert's answer
2020-10-23T07:20:26-0400

solution


Present value of benefits at retirement

"Duration\\ n=10\\ years"

"Payments\\ p= 60,000"

"Interest\\ r=0.06"


Compounding is done quarterly. Therefore, the effective annual rate is



"i= (1+\\frac{0.06 }{4 })^4-1=0.061364"




"A= p * \\frac{1-(1+i)^{{-n}} }{i}"


"= 60,000 * \\frac{1-(1.061364)^{-10} }{0.061364}= \n438,766.34272"

The deposits to be accumulated quarterly (every three months) should equal 438766.34272



"A = c \\ * \\frac{(1+\\frac{r}{4})^{t*4}-1}{\\frac{r}{4} }"


"438,766.34272 = c \\ * \\frac{(1+\\frac{0.06}{4})^{25*4}-1}{\\frac{0.06}{4} }"

"438,766.34273= 228.803*c"

"C= 1,917.6596"

Answer. He must deposit $ 1,917.6596

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