Frank opened a savings account with $700 at 4.5 percent interest, compounded quarterly, and kept it in the account for two years. How much was the final amount?
.045/4 = .01125 per quarter for 8 quarters
700 (1.01125)^8 = 765.54
To calculate the final amount in Frank's savings account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years the money is invested
In this case, Frank's initial deposit (P) is $700, the annual interest rate (r) is 4.5% (or 0.045 as a decimal), the interest is compounded quarterly (n = 4), and the money is invested for 2 years (t = 2).
Now we can substitute these values into the formula:
A = 700(1 + 0.045/4)^(4*2)
Calculating further:
A = 700(1 + 0.01125)^8
A = 700(1.01125)^8
A ≈ 700(1.092204)
A ≈ 763.54
Therefore, the final amount in Frank's savings account after two years would be approximately $763.54.