To find the number of years it takes for an investment to grow to a certain amount using compound interest, you can use the formula A = P(1 + r/n)^nt. In this case, it will take about 7.54 years for an investment of $3,400 with an annual interest rate of 1.7% compounded annually to grow to $4,150.
To calculate the number of years it takes for an investment to grow to a certain amount using compound interest, you can use the formula:
A = P(1 + r/n)nt
Where:
- A is the final amount
- P is the initial investment
- r is the annual interest rate (expressed as a decimal)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, you have $3,400 and want to find how many years it takes for the investment to grow to $4,150 with an annual interest rate of 1.7% (0.017) compounded annually. Plug the given values into the formula and solve for t:
4150 = 3400(1 + 0.017/1)1t
Divide both sides of the equation by 3400:
(1 + 0.017/1)t = 4150/3400
Simplify the right side:
(1 + 0.017/1)t = 1.22
Take the logarithm of both sides using the natural logarithm (ln):
t ln(1 + 0.017/1) = ln(1.22)
Divide both sides by ln(1 + 0.017/1):
t = ln(1.22) / ln(1 + 0.017/1)
Use a calculator to find the value of t, which is approximately 7.54. So, it will take about 7.54 years for the investment to grow to $4,150.