You deposit $5,000 in an account earning 7.5% interest compounded semiannually. How much will you have in the account after 9 years?
(Note: Use n=12 for monthly compounding, n=4 for quarterly compounding, n=2 for semiannual compounding, and n=1 for annual compounding.)
amount=5000(1+ (i/n))^(t*n)
where n is the number of compounds per year, and t=9
for instance, for n=12, put this in your google search window:
5000(1+(.075/12))^(9*12)=
And the answer pops up 9799.56
To calculate the future value of the account after 9 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the initial deposit or principal amount ($5,000 in this case)
r = annual interest rate (7.5% or 0.075 as a decimal)
n = number of times compounded per year (2 for semiannual compounding)
t = number of years (9 in this case)
Plugging in the values into the formula, we have:
A = 5000(1 + 0.075/2)^(2*9)
Simplifying the calculations step by step:
1. Divide the annual interest rate by the number of times compounded per year:
0.075/2 = 0.0375
2. Multiply the number of times compounded per year by the number of years:
2 * 9 = 18
3. Add 1 to the result from step 1:
1 + 0.0375 = 1.0375
4. Raise the result from step 3 to the power of the result from step 2:
1.0375^18 ≈ 2.0363
5. Multiply the initial deposit by the result from step 4 to get the future value of the account:
5000 * 2.0363 ≈ $10,181.50
So, you would have approximately $10,181.50 in the account after 9 years.