Question

1400 dollars is placed in an account with an annual interest rate of 5.5%. to the nearest year, how long will it take for the account value to reach 2900 dollars?

Answer 1

It will take 19 years and 6 months for the account value to reach 2900 dollars

Step-by-step explanation:

Given

Principal amount = 1400 dollars

Rate = 5.5 %

Final value = A = 2900

We have to find t

So,

The formula for simple interest is:

$A = P(1+rt)$

Putting values

$2900 = 1400(1+0.055.t)\\\frac{2900}[1400} = 1+0.055t\\2.071 = 1+0.055t\\2.071-1=0.055t\\1.071 =0.055t$

Dividing both sides by 0.055

$\frac{0.055t}{0.055} = \frac{1.071}{0.055}\\t = 19.47\ years$

Rounding off to nearest tenth

19.5 years

Hence,

It will take 19 years and 6 months for the account value to reach 2900 dollars

Keywords: Interest, simple interest

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