I keep getting an answer with an exponent and i am not sure what i have done wrong here. Any help is appreciated.
To save for his retirement, Jeff puts $800 per month into his savings account every month for 30 years. The savings account pays 9% interest compounded monthly. How much money will he have in his savings account when he retires at the end of those 30 years?
FV=?
i=0.045
n=360
R=800
FV=R[(1+i)^n-1]/i
FV=800[(1+0.045)^360-1]/0.045
FV=800[7618413.852-1]
FV=800(7618412.852)/0.045
FV=1.354384507^11
Your errors include
i is .09/12=.0075
I get 1.46million dollars, about.
Thanks for your help.!
Actually, if you do simple math, you would get $25,920. If you want to know how much he will have after cashing it in, just do this.
I=PRT
I is the simple interest = 25,920
P is the Principal = $800
R is the rate = 9% = 0.09
T is the time = 30 years = 360 months
800x0.09x360=25,920
To find the amount of money Jeff will have in his savings account when he retires, you correctly used the formula for future value (FV) of a series of regular deposits with compound interest:
FV = R[(1+i)^n-1]/i
Now let's go through the calculations step by step:
1. R represents the regular deposit amount, which in this case is $800 per month.
2. i represents the interest rate per compounding period, which is 9% or 0.09 per year. However, since the interest is compounded monthly, you need to divide the annual interest rate by 12 to get the monthly interest rate. So i = 0.09/12 = 0.0075.
3. n represents the number of compounding periods, which is the number of months Jeff saves for retirement. In this case, Jeff saves for 30 years, so n = 30 years x 12 months/year = 360 months.
Now, let's plug in these values into the formula:
FV = 800[(1+0.0075)^360-1]/0.0075
= 800[(1.0075)^360-1]/0.0075
The exponential part is where you encountered the exponent. However, you made a mistake in calculating it. Instead of calculating 1.0075 raised to the power of 360, you wrote 1.354384507^11. Let's correct that part:
FV = 800[(1.0075)^360-1]/0.0075
≈ 800(2.9806928008-1)/0.0075
≈ 800(1.9806928008)/0.0075
≈ 211,654.10
Therefore, Jeff will have approximately $211,654.10 in his savings account when he retires at the end of those 30 years.