Problema Solution
A principal of $7500 is invested in an account paying an annual rate of 7%. Find the amount in the account after 4 years if the account is compounded semi annually, quarterly, and monthly.
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when the account is compounded semi annually
A = the future value after 4 years
P = $7500 is the principal
t = 4 year the number of years
m = 2 the number of compounding periods per year (semiannually)
n = m*t = 2*4 = 8 the number of compounding periods
r = 0.07 or 7% the annual interest rate
i = r/m = 0.07/2 = 0.035 interest rate per period
A = P(1 + i)^n
A = 7500(1 + 0.035)^8
A = $9876.0678
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when the account is compounded quarterly
A = the future value after 4 years
P = $7500 is the principal
t = 4 year the number of years
m = 4 the number of compounding periods per year (semiannually)
n = m*t = 4*4 = 16 the number of compounding periods
r = 0.07 or 7% the annual interest rate
i = r/m = 0.07/4 = 0.0175 interest rate per period
A = P(1 + i)^n
A = 7500(1 + 0.0175)^16
A = $9899.47012
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when the account is compounded monthly
A = the future value after 4 years
P = $7500 is the principal
t = 4 year the number of years
m = 12 the number of compounding periods per year (semiannually)
n = m*t = 12*4 = 48 the number of compounding periods
r = 0.07 or 7% the annual interest rate
i = r/m = 0.07/12 interest rate per period
A = P(1 + i)^n
A = 7500(1 + 0.07/12)^48
A = $9915.4041
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