Problema Solution
A principal of $6500 is invested in an account paying an annual rate of 7%. Find the amount in the account after 6 years if the account is compounded semiannually, quarterly, and monthly.
A: Semiannually amount
B:Quarterly amount
C:Monthly amount.
Answer provided by our tutors
P = $6500 the principal
r = 0.07 or 7% annual interest rate
t = 6 years
A = the future value (the amount in the account after 6 years)
A: Semiannually amount
m = 2 compounding period per year
i = 0.07/2 = 0.035 interest rate per period
n = 6*2 = 12 total number of compounding periods
A = future value
A = P(1 + i)^n
A = 6500(1 + 0.035)^12
A = $9,821.95
B: Quarterly amount
m = 4 compounding period per year
i = 0.07/4 = 0.0175 interest rate per period
n = 6*4 = 24 total number of compounding periods
A = future value
A = P(1 + i)^n
A = 6500(1 + 0.0175)^24
A = $9,856.88
C: Monthly amount
m = 12 compounding period per year
i = 0.07/12 interest rate per period
n = 6*12 = 72 total number of compounding periods
A = future value
A = P(1 + i)^n
A = 6500(1 + 0.07/12)^72
A = $9,880.68