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
P = $5,000
r = 0.14 annual interest rate
t = 5 years
m = 2 compounding periods per year
i = r/m = 0.14/2 = 0.07 interest rate per period
n = t*m = 5*2 = 10 total number of compounding periods
A = the future value
A = P(1 + i)^n
A = 5000(1 + 0.07)^10
the future amount A now becomes a principal P for the next 4 years
P = 5000(1 + 0.07)^10
r = 0.11
t = 4 years
m = 1
i = 0.11
n = 4
A = 5000(1 + 0.07)^10 *(1 + 0.11)^4
the future amount A now becomes a principal P for the last 6 years
P = 5000(1 + 0.07)^10 *(1 + 0.11)^4
r = 0.10
t = 6 years
m = 4
i = 0.10/4 = 0.025
n = 6*4 = 24
A = 5000(1 + 0.07)^10 *(1 + 0.11)^4 * (1 + 0.025)^24
by solving we find
A = $27,006.7588
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the amount due at the end of 15 years will be $27,006.7588.