A principle of $2400 is invested at 7.5% interest, compounded annually. How many years will it take to accumulate $6000 or more in the account? Write the smallest possible whole number answer.

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Mathematics

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9 July, 22:15

A principle of $2400 is invested at 7.5% interest, compounded annually. How many years will it take to accumulate $6000 or more in the account? Write the smallest possible whole number answer.

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Chelsea Hines · Answer 1

Step-by-step explanation:To find the interest accumulated over a period of time you use:

A = P [1 + (r/n) ]^ (nt)

with A = new amount in the account, P = principal, r = percent rate as a decimal, n = how many times you compound during one year, t = time in years.

A = 2000

P = 1500

r = 0.035

n=1

Thus you get:

2000 = 1500 (1+0.035) ^t

Divide by 1500:

(4/3) = (1.035) ^t

Apply "ln" on both sides:

ln (4/3) = t*ln (1.035)

Calculate the logarithms:

0.28768 = t*0.03440

Divide by 0.03440 on both sides:

t = 8.36 years

So after approximately 8 years and 5 month you will have $2000 or more in the account.