suppose that $5000 is invested in an account with APR of 12% compounded monthly. find the future value of the account in 5 years.
New Value of account= $5000*(1+12/100)^5
= $8811.7
That is the amount compounded annually.
Compounded monthly you get
5000(1+.12/12)^(12*5) = 9083.43
To find the future value of the account after 5 years with a 12% APR compounded monthly, we can use the formula for compound interest:
Future Value = Principal * (1 + (APR / n))^(n*t)
Where:
Principal = $5000 (initial investment)
APR = 12% (annual interest rate)
n = 12 (number of times interest is compounded per year)
t = 5 (number of years)
Now we can substitute these values into the formula and calculate the future value:
Future Value = $5000 * (1 + (0.12 / 12))^(12*5)
Step 1: Divide the annual interest rate by the number of times interest is compounded per year:
APR / n = 0.12 / 12 = 0.01
Step 2: Calculate the exponent:
n*t = 12 * 5 = 60
Step 3: Plug the values into the formula:
Future Value = $5000 * (1 + 0.01)^60
Step 4: Calculate:
Future Value = $5000 * (1.01)^60
Using a calculator or a spreadsheet, the future value can be calculated as follows:
Future Value = $5000 * (1.01)^60
= $5000 * 1.790847878
= $8954.24
Therefore, the future value of the account after 5 years will be approximately $8,954.24.
To find the future value of the account after 5 years, we can use the formula for compound interest:
\(A = P(1 + \frac{r}{n})^{nt}\)
Where:
A = Future value of the account
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
In this case, the principal amount (P) is $5000, the annual interest rate (r) is 12% or 0.12, and the interest is compounded monthly, so the number of times compounded per year (n) is 12. The investment period (t) is 5 years.
Let's plug in the values into the formula to calculate the future value of the account:
\(A = 5000(1 + \frac{0.12}{12})^{12 \times 5}\)
First, simplify the fraction inside the parentheses:
\(A = 5000(1 + 0.01)^{12 \times 5}\)
Next, calculate the value inside the parentheses:
\(A = 5000(1.01)^{12 \times 5}\)
Raise 1.01 to the power of \(12 \times 5\) (multiply the exponent):
\(A = 5000(1.01)^{60}\)
Using a scientific calculator or spreadsheet, calculate the value of \((1.01)^{60}\) which should be approximately 1.795856:
\(A = 5000 \times 1.795856\)
Multiply the principal amount by this value to get the future value of the account:
\(A = 8979.28\)
Therefore, the future value of the account after 5 years will be approximately $8979.28.