What nominal rate converted semi-annually will make P40,000 accumulate to P100,000 in 8 years?
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What nominal rate converted semi-annually will make P40,000 accumulate to P100,000 in 8 years?
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Answer:
find the nominal rate that will make P40,000 accumulate to P100,000 in 8 years, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial amount (P40,000)
r = the nominal rate
n = the number of compounding periods per year (semi-annually = 2)
t = the number of years (8)
We can rearrange the formula to solve for r:
r = n[(A/P)^(1/nt) - 1]
Plugging in the given values, we get:
r = 2[(100,000/40,000)^(1/8*2) - 1]
Solving for r gives us 0.0844 or 8.44%.
So, a nominal rate of 8.44% compounded semi-annually will make P40,000 accumulate to P100,000 in 8 years.