An initial deposit of $900 earns 13% interest, compounded monthly. How much will be in the account in 7 1/2
years? (Round your answer to the nearest cent.)
just use your formula...
900(1 + 0.13/12)^(12*7.5) = 2373.57
To find the amount in the account in 7 1/2 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = amount in the account
P = principal (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $900
r = 13% = 0.13
n = 12 (compounded monthly)
t = 7.5 years
Substituting these values into the formula:
A = 900(1 + 0.13/12)^(12*7.5)
Calculate:
A ≈ 900(1 + 0.01083)^(90)
A ≈ 900(1.01083)^(90)
A ≈ 900 * 2.156754
A ≈ $1,941.08
Therefore, the amount in the account after 7 1/2 years will be approximately $1,941.08.
To calculate the amount in the account after 7 1/2 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the principal (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = time in years
In this case, the principal (P) is $900, the annual interest rate (r) is 13% or 0.13 in decimal form, the interest is compounded monthly, so the number of times interest is compounded per year (n) is 12, and the time (t) is 7 1/2 years or 7.5 years.
Plugging in these values into the formula:
A = 900(1 + 0.13/12)^(12*7.5)
Now we can solve this calculation.