You will be receiving $5,000 from your family as a graduation present. You have decided to save this money for your retirement. You plan to retire thirty years after graduating. How much additional money will you have at that time if you can earn an average of 9 percent on your investment instead of just 8 percent? (Round to the nearest dollar)
difference
= 5000( 1.09^30 - 1.08^30)
= $16,025.11
Thank you very much Reiny~
To calculate the additional money you will have at retirement by earning an average of 9 percent instead of 8 percent, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Total amount at the end of the investment period
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years the money is invested for
Given:
Principal amount (P) = $5,000
Annual interest rate (r) for 8 percent = 0.08
Annual interest rate (r) for 9 percent = 0.09
Number of times interest is compounded per year (n) = 1
Number of years (t) = 30
For an 8 percent interest rate:
A1 = 5000(1 + 0.08/1)^(1*30)
= 5000(1.08)^30
= $32,071.29
For a 9 percent interest rate:
A2 = 5000(1 + 0.09/1)^(1*30)
= 5000(1.09)^30
= $36,621.49
The additional money you will have at retirement by earning an average of 9 percent instead of 8 percent is:
A2 - A1 = $36,621.49 - $32,071.29
= $4,550.20
Therefore, you will have approximately an additional $4,550 at retirement by earning an average of 9 percent instead of 8 percent.
To calculate the additional money you will have at retirement by earning an average of 9 percent instead of 8 percent, you can follow these steps:
1. Calculate the future value of the $5,000 investment after 30 years:
FV = PV * (1 + r)^n
where FV is the future value, PV is the present value, r is the rate of return, and n is the number of periods.
FV at 8 percent = $5,000 * (1 + 0.08)^30 = $5,000 * (1.08)^30 = $31,355.92 (rounded to the nearest cent).
2. Calculate the future value of the $5,000 investment after 30 years at an average rate of 9 percent:
FV at 9 percent = $5,000 * (1 + 0.09)^30 = $5,000 * (1.09)^30 = $36,842.23 (rounded to the nearest cent).
3. Calculate the additional money by subtracting the future value at 8 percent from the future value at 9 percent:
Additional Money = FV at 9 percent - FV at 8 percent
Additional Money = $36,842.23 - $31,355.92 = $5,486.31 (rounded to the nearest cent).
Therefore, if you can earn an average of 9 percent on your investment instead of 8 percent, you will have approximately $5,486 (rounded to the nearest dollar) as additional money at retirement.