This is the question: "If you want to have $75,000 after 35 years in your account that pays 12% annual interest compounded quarterly, how much should you put in as your original investment?" The formula I'm using is y=a(1+r)^t, with a being the initial amount, r being the rate in decimal form, and t is time relative to the rate. Or y=a(1+r/t)^t Although my biggest problem is that I'm not sure whether to have the 1+r or 1−r. So after plugging in what I have either: 75000=a(1−.12)^35 75000=a(1+.12)^35 or you can use this formula (preferably): 75000=a(1−.12/35)^35 75000=a(1+.12/35)^35

Deacon House

Deacon House

Answered question

2022-09-05

This is the question: "If you want to have $75,000 after 35 years in your account that pays 12% annual interest compounded quarterly, how much should you put in as your original investment?"
The formula I'm using is y = a ( 1 + r ) t , with a being the initial amount, r being the rate in decimal form, and t is time relative to the rate. Or y = a ( 1 + r / t ) t
Although my biggest problem is that I'm not sure whether to have the 1+r or 1−r.
So after plugging in what I have either:
75000 = a ( 1 .12 ) 35
75000 = a ( 1 + .12 ) 35
or you can use this formula (preferably):
75000 = a ( 1 .12 / 35 ) 35
75000 = a ( 1 + .12 / 35 ) 35

Answer & Explanation

Conner Singleton

Conner Singleton

Beginner2022-09-06Added 13 answers

Suppose I deposit X dollars and leave it for say 25 interest-periods gaining 5% per interest period.
Then the amount in my account at the end of that process is X(1.05)25=3.386X
If I know the amount at the end of the period, Y=3.386X then obviously I can find out what X was also. Say the resulting amount is $45000 - then the original deposit was
450003.386→ $13288.63
Your problem is exactly like this - you just have extra steps to calculate what the interest rate is and how many interest periods you are talking about.

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