Question

Kira deposited $3000 into an account with a 3.4% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $4500? Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

The time it will take for the investment to grow to $4500 is 11.97 years

Compound interest

The formula for calculating the compound interest is expressed according to the formula

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

Given the following parameters

P0 = $3000

rate = 3.4%

time = t

P(t) = 4500

n = 4

Substitute

4500 = 3000(1+0.034/4)^4t
45/30 = 1.0085^4t

1.5 =  1.0085^4t

ln1.5 = 4tln1.0085

4t = ln1.5/ln1.0085

4t = 47.904

t = 11.97

Hence the time it will take for the investment to grow to $4500 is 11.97 years

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