Calculate, to the nearest cent, the future value FV of an investment of $10,000 at the stated interest rate after the stated amount of time. HINT [See Example 1.]
5% per year, compounded daily (assume 365 days/year), after 11 years
work:10,000(1+0.05/365)^(365)(11)=17331.87
this is the answer i got but i keep getting it wrong
V = Vo(1+r)^n
r = 5%/365/100% = 0.00013699 = Daily %
rate expressed as a decimal.
n = 365Comp./yr * 11Yrs = 4015 Compounding periods.
V = 10,000(1.00013699)^4015 = $17,332.13
To calculate the future value of an investment using compound interest, you can use the formula:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, we have:
P = $10,000
r = 0.05 (5% as a decimal)
n = 365 (compounded daily)
t = 11 years
Plugging in the values into the formula, we get:
FV = $10,000(1 + 0.05/365)^(365)(11)
Using a calculator, the calculation is as follows:
FV = $10,000(1 + 0.000136986301369863)^4025
FV = $10,000(1.000136986301369863)^4025
FV = $10,000(1.698738)
FV ≈ $16,987.38
Therefore, the future value of the investment after 11 years, compounded daily at a 5% annual interest rate, is approximately $16,987.38 to the nearest cent.
Your calculation is correct, but you may be rounding your answer incorrectly. Let's double-check the calculation together.
The formula for compound interest is:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value
PV = Present Value (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, the given values are:
PV = $10,000
r = 5% (0.05 as a decimal)
n = 365 (compounded daily)
t = 11 years
Now apply the values to the formula:
FV = 10,000 * (1 + 0.05/365)^(365*11)
First, divide the annual interest rate by the number of compounding periods per year:
0.05/365 ≈ 0.00013699
Next, multiply the number of compounding periods per year by the number of years:
365 * 11 = 4,015
Now substitute these values into the formula:
FV = 10,000 * (1 + 0.00013699)^4,015
Using a calculator, evaluate the expression inside the parentheses, and then multiply it by the initial investment:
FV ≈ 10,000 * 1.66507
Finally, round your answer to the nearest cent:
FV ≈ $16,650.70
So, the future value of the $10,000 investment at an interest rate of 5%, compounded daily for 11 years, is approximately $16,650.70.