Question

What annual compound interest rate is required for an investment to grow by 54% in 10 years if interest is compounded 147 times per year?

Round your answer to the nearest tenth of a percent.

Answer 1

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the future value of the investment

P = the principal amount invested

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the number of years

We know that A/P = 1 + 54% = 1.54, t = 10 years, and n = 147. We can solve for r by substituting the given values:

1.54 = (1 + r/147)^(147*10)

ln(1.54) = ln[(1 + r/147)^(147*10)]

ln(1.54) = 147*10*ln(1 + r/147)

ln(1.54) / (147*10) = ln(1 + r/147)

e^(ln(1.54) / (147*10)) = 1 + r/147

e^(ln(1.54) / (147*10)) - 1 = r/147

147[e^(ln(1.54) / (147*10)) - 1] = r

Using a calculator, we get:

r ≈ 0.0509

Therefore, the annual compound interest rate required for the investment to grow by 54% in 10 years if interest is compounded 147 times per year is approximately 5.1%.