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.

deefranklin Sep 30, 2021

#1**0 **

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?

deefranklin Sep 30, 2021

#2**+2 **

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)

ElectricPavlov Sep 30, 2021

#3**+2 **

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

ElectricPavlov Sep 30, 2021