How do I do this?

Question

Lena needs $5360

 for a future project. She can invest $5000

 now at an annual rate of 4%

, compounded quarterly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?

Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

5360=5000(1+.04/4)^4t

536/500=1.072= 1.01^4t

1.072=(1.01^t)^4= 1.072

1.01^t= 4th root of 1.072=1.017533453

t = log_1.011.1017533453= ln1.017533453/ln1.01

=.017381515/.00995= .017381515(100.4991708)=1.746827845

t = about 1.75 years

= about 1 year 9 months

check the answer

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

where n= number of compounding periods per year

and t=time in years, r=rate of annual interest, P=Principal, A=ending Amount

= 5000(1+.04/4)^4t

=5000(1.01)^4(1.75)

=5000(1.01^7)

=5000(1.072135352

=about 5360.677

=about $5,360