Find how many years it would take for an investment of $3700 to grow to $6000 at an annual interest rate of 6.2% compounded semi

Question

2 years ago

5

-annually.

1 answer:

lorasvet [3.4K] · Answer 1 · 2022-08-23T06:21:54+03:00

Answer:

7 years 11 months

Step-by-step explanation:

The future value formula for the value of a principal P invested at annual rate r compounded n times yearly for t years is ...

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

For the given numbers, we want to find t:

6000 = 3700(1 +.062/2)^(2t)

Dividing by 3700 and taking the logarithm, we get ...

6000/3700 = 1.031^(2t)

log(60/37) = 2t·log(1.031)

Dividing by the coefficient of t gives ...

t = log(60/37)/(2log(1.031)) ≈ 7.92 . . . . . years

It will take about 7 years 11 months for the investment to grow to $6000.