Question

(1 point) How long do you need to invest your money in an account earning an annual interest rate of 3.824%3.824% compounded weekly so that your investment grows from $1,348.85$1,348.85 to $10,275.00$10,275.00 over that period of time?

Answer 1

We use the formula:
A=P(1+r/52)^52n
where
A=future value
P=present value
r=rate of interest
n=time period.

10275=1348.85*(1+0.03824/52)^52n

(10275/1348.85)=(1+0.03824/52)^52n

Taking log on both sides;

log (10275/1348.85)=52n*log 1.000735385

n=1/52[log (10275/1348.85)/log 1.000735385]

which is equal to

=53.12 years(Approx).