Tom Invested $7,000 at 6.5% interest compounded monthly. How much will be in this account after 18 months?
P = Po * (1+r)^n
r = (6.5%/12)/100% = 0.00542 = Monthly
% rate expressed as a decimal.
n = 1Comp./mo * 18mo = 18 Compounding
periods.
Solve for P.
To find out how much will be in Tom's account after 18 months with a compounded monthly interest rate of 6.5%, we can use the formula for compound interest:
A = P*(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Given:
P = $7,000
r = 6.5% = 0.065 (converted to decimal)
n = 12 (compounded monthly)
t = 18 months / 12 months per year = 1.5 years
Now let's plug these values into the formula:
A = 7000 * (1 + 0.065/12)^(12*1.5)
To calculate the result, we need to break it down into steps:
Step 1: Calculate the exponent
12 * 1.5 = 18
Step 2: Calculate the base inside the parentheses
1 + 0.065/12 = 1.00541666667
Step 3: Raise the base to the power of the exponent
(1.00541666667)^18 ≈ 1.1056096263
Step 4: Multiply the principal by the result from step 3
A = 7000 * 1.1056096263 ≈ $7,739.27
Therefore, after 18 months, there will be approximately $7,739.27 in Tom's account.