Problema Solution
Find the amount due at the end of 15 years if P 5,000 is invested at 14% compounded semi-annually for the first 5 years, 11% compounded annually for the next 4 years and 10% compounded quarterly for the last 6 years.
Answer provided by our tutors
P1 = $5,000 principal
r = 0.14 annual interest rate
m = 2 number of compounding periods per year
t = 5 years
n = m*t = 10 number of compounding periods
i = r/m = 0.14/2 = 0.07 interest rate per period
A1 = the future value
A1 = P1(1 + i)^n
A1 = 5000(1 + 0.07)^10
this amount will be the new principal for the next 4 years
P2 = A1
r = 0.11 annual interest rate
m = 1 number of compounding periods per year
t = 4 years
n = m*t = 4 number of compounding periods
i = r/m = 0.11 interest rate per period
A2 = the future value
A2 = P2(1 + i)^n
A2 = 5000(1 + 0.07)^10(1 + 0.11)^4
this amount will be the new principal for the last 6 years
P3 = A2
r = 0.10 annual interest rate
m = 4 number of compounding periods per year
t = 6 years
n = m*t = 24 number of compounding periods
i = r/m = 0.10/4 = 0.025 interest rate per period
A3 = the future value
A3 = P3(1 + i)^n
A3 = 5000(1 + 0.07)^10(1 + 0.11)^4 (1 + 0.025)^25
A3 = $27,681.93
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the amount due at the end of 15 years is $27,681.93.