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# a Question

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John is 25 years old and wants to have 1 million dollars in savings by the time he retires at 65. He plans to open a savings account that pays 4% interest compounded quarterly and he will be making \$200 quarterly deposits into the account.

Sep 30, 2021

#1
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Suppose you invest \$150 a month for 8 years into an account earning 9% compounded monthly. After 8 years, you leave the money, without making additional deposits, in the account for another 29 years. How much will you have in the end?

Sep 30, 2021
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John is 25 years old and wants to have 1 million dollars in savings by the time he retires at 65. He plans to open a savings account that pays 4% interest compounded quarterly and he will be making \$200 quarterly deposits into the account.

You are looking for the future value of an ordinary annuity   at 40 years from now

period = 4 / year      total periods = 40 * 4 = 160 periods = n

Interest per period = .04 / 4 = .01    =   i

payments = 200 per period

FV = pmt *{ (1 +i)n -1}/ i      =  78,276.53    <===== well short of 1 000 000   that he wants !  (he needs to deposit 2555.04 per quarter)

Sep 30, 2021
#3
+35238
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Suppose you invest \$150 a month for 8 years into an account earning 9% compounded monthly. After 8 years, you leave the money, without making additional deposits, in the account for another 29 years. How much will you have in the end?

Assuming the money is put into the account at THE BEGINNING of the month

FV = pmt { (1+i)^n -1)/i }   * (1+ i )          n = 8 * 12 = 96     i = .09/12    pmt = 150

= 21135.76    after 8 years

then   21 135.76 ( 1.0075) 29*12  =284 640 .66

Assuming the money is put into the account at THE END of the month

pmt { ((1+i)n -1)/i) }  = 20978.42

then   20978.42 (1.0075)29*12  = 282 521 .79

Sep 30, 2021