Answer to Question #282222 in Financial Math for cacan

Question

If P20,000 will accumulate to P45,758.55 in 4 years, what is the interest rate compounded semi-annually?

Answer 1

$A=P(1+\frac {r} {100}) ^n$

$45,758.55=20,000(1+\frac {r} {100}) ^8$

$\frac {45,758.55} {20,000} =(1+\frac {r} {100}) ^8$

$2.2879 =(1+\frac {r} {100}) ^8$

$\sqrt[8] {2.2879} =\sqrt[8] {(1+\frac {r} {100}) ^8}$

$1.109=1+\frac {r} {100}$

$0.109=\frac {r} {100}$

$r=10.9\%×2$

r=21.8%