Question

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

Answer 1

for compounded interest rate:

$P=R(1+\frac i n)^{n*t}\implies i=n*(({\frac P R})^{\frac 1 {n*t}}-1)$ , where P - current amount, R - initial amount, i - annual interest rate, n - number of payments in one year, t - number of years

In 1 year there will be 2 payments if payments are semi-annualy. So

$i=2*(({\frac {45758.75} {20000}})^{\frac 1 {2*4}}-1)\approx21.8$

approximately 21.8%