How much money will there be in an account at the end of 8yrs if $5000 is deposited at 7% interest compounded semi annually?
What is 5000(1.035)^16 ?
$8669.93
correct
To calculate the amount of money in an account at the end of a certain period with compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount in the account at the end of the time period
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $5000, the annual interest rate (r) is 7% or 0.07, and the interest is compounded semiannually, so the number of times interest is compounded per year (n) is 2. The time period (t) is 8 years.
Plugging the values into the formula:
A = 5000(1 + 0.07/2)^(2*8)
First, divide the annual interest rate (0.07) by the number of times compounded per year (2). This gives us an interest rate per compounding period of 0.07/2 = 0.035.
Next, multiply the number of compounding periods per year (2) by the number of years (8) to get 2*8 = 16.
Now, raise the value inside the parentheses (1 + 0.035) to the power of 16:
A = 5000(1.035)^16
Using a calculator or a computer program, calculate (1.035)^16 = 1.703275. Multiplying this value by the initial deposit:
A = 5000 * 1.703275
A = $8,516.38
Therefore, there will be approximately $8,516.38 in the account at the end of 8 years.