If $8,500 is deposited in a compound interest account paying 3.9% interest annually, how much will be in the account after 12 years?
Pt = Po(1+r)^n.
r = 3.9% / 100% = 0.039=APR expressed
as a decimal.
n = 1comp/yr * 12yrs.=12 Compounding
periods.
Pt = 8500(1.039)^12 = $13,452.58.
To calculate the amount in the compound interest account after 12 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount in the account after time t
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case:
P = $8,500
r = 3.9% = 0.039 (decimal form)
n = 1 (compounded annually)
t = 12 years
Substituting these values into the formula:
A = 8500(1 + 0.039/1)^(1*12)
Simplifying the equation gives:
A = 8500(1 + 0.039)^(12)
Calculating the values within the parentheses as powers:
A = 8500(1.039)^12
Using a calculator, we can evaluate (1.039)^12 as approximately 1.4849. So the equation becomes:
A = 8500 * 1.4849
Solving this gives:
A ≈ $12,614.65
Therefore, the amount in the account after 12 years will be approximately $12,614.65.