$4000 is deposited into an account earning j₂ = 8% for the first 2 years and j₂ = 10% thereafter.How long will it take for it to grow to $9041.67? A)6 yrs,9 months B)8 yrs,9 months C)13 yrs,6 months D)17 yrs,6 months

Question

Quizplus · Accepted Answer

For the first 2 years, the interest rate is 8%, which means the amount after 2 years will be:

4000 * (1 + 0.08)^2 = 4646.72

From year 3 onwards, the interest rate is 10%, so we can use the formula for compound interest:

9041.67 = 4646.72 * (1 + 0.1)^n

where n is the number of years from the end of year 2.

Simplifying the equation, we get:

1.944 = 1.1^n

Taking the logarithm of both sides, we get:

n = log(1.944) / log(1.1) = 8.75

So it will take approximately 8 years and 9 months for the account to grow to $9041.67. Therefore, the correct answer is B.

$4000 Is Deposited into an Account Earning J2 = 8

$4000 Is Deposited into an Account Earning J₂ = 8