how long is the money

Question

For her birthday, Lexi's parents gave her $5,575.00 which they put into a savings account that earns 9% interest compounded annually. When Lexi started college, she withdrew the entire balance of $9,521.00 and used it to pay for tuition. How long was the money in the account?

Answer 1

A = p(1+r/n)^nt

A = final amount = 9521

p = principal = 5575

r = interest rate = 9% = 0.09

n = # times compounded per year = 1

t = time in years

 

Plug all the values into the formula:

 

9521 = 5575(1+0.09/1)^1t

9521 = 5575(1.09)^t

9521/5575 = 1.09^t

Take log of both sides

log(9521/5575) = log 1.09^t

 

log(9521/5575) = t(log 1.09)

 

t = [log(9521/5575)]/(log 1.09)

 

t = 6.21 years

 

(0.21 years)(12 months/year) = 2.5 months

 

t = 6 years 2.5 months

 

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