If $695 is invested in an account that earns 21.75%, compounded annually, what will the account balance be after 15 years? (Round your answer to the nearest c
P = Po(1+r)^n.
r = 21.75% / 100% = 0.2175 = Annual %
rate expressed as a decimal.
n = 1Comp./yr * 15yrs = 15 Compounding
periods.
P = 696(1.2175)^15 = $13,305.14.
To find the account balance after 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future account balance
P = the initial principal (or investment amount)
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the money is invested for
In this case, the initial principal (P) is $695, the annual interest rate (r) is 21.75% or 0.2175 (expressed as a decimal), the interest is compounded annually (n = 1), and the investment period (t) is 15 years.
Substituting these values into the formula, we get:
A = 695(1 + 0.2175/1)^(1*15)
Now let's calculate the answer step by step:
Step 1: Calculate the inside of the brackets first:
(1 + 0.2175/1) = 1.2175
Step 2: Calculate the exponent:
(1.2175)^(1*15) = 1.2175^15
Step 3: Calculate the final account balance:
A = 695 * 1.2175^15
Using a calculator, we find that A is approximately $5,588.55.
Therefore, the account balance after 15 years, rounded to the nearest cent, is $5,588.55.