Question

if tzs 2,500,000 is invested at an interest rate of 9.5%,compounded twice monthly, how long will it take for the investment to reach tzs 7,500,000?​

Answer 1

9514 1404 393

Answer:

  11 years, 7 months

Step-by-step explanation:

When the investment reaches its desired value, it will be 3 times the original amount. So, we are looking for the number of half-month periods (n) of compounding such that ...

  (1 +0.095/24)^n = 3

Taking logarithms, we have ...

  n·log(1.003958333...) = log(3)

  n = log(3)/log(1.009358333...) ≈ 278.09

This is 278.09/24 ≈ 11.59 years.

It will take about 11 years and 7 months for the investment to reach the desired value.

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Additional comment

The amount will be about tzs 2,758 short after 11 years 7 months. It will exceed the desired amount after 2 more days' interest is added.