Sam Monte deposits $21,500 into Legal Bank which pays 6 percent interest that is compounded semiannually. By using the table in the handbook, what will Sam have in his account at the end of 6 years?
The formula for compound interest is:
A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, t is the time in years, r is the interest rate, and n is how many times a year it is compounded.
A = 21,500(1 + 0.06/2)^(2*6)
Solve from there.
He borrowed $500 for seven months and paid 53.96 in interest. what was the rate of interest?
To calculate the amount Sam will have in his account at the end of 6 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (in this case, $21,500)
r = the annual interest rate (6% or 0.06)
n = the number of times the interest is compounded per year (semiannually means twice a year)
t = the number of years (6 years)
First, we need to determine the value of (1 + r/n)^(nt) using the table in the handbook.
For semiannual compounding, n is 2 (twice a year), and t is 6 (6 years). We plug these values into the formula:
(1 + r/n)^(nt) = (1 + 0.06/2)^(2*6)
Now, let's calculate that value.
(1 + 0.06/2)^(12) = 1.03^(12)
Using a calculator or spreadsheet, we find that (1.03)^(12) ≈ 1.4295.
Now, we can calculate the future value of the investment using the compound interest formula:
A = P * (1.4295)
A = $21,500 * 1.4295
A ≈ $30,732.25
Therefore, at the end of 6 years, Sam will have approximately $30,732.25 in his account.