Problema Solution
If $8,000 is placed in an account with an annual interest rate of 3%, how long will it take the amount to quadruple if the interest is compounded annually?
Answer provided by our tutors
Use compounded interest Formula:
A=P(1+i/n)nt
A=Final amount with interest compounded
P=Principle Amount
n= number of times interest in compounded
P=$8000
i=3%=0.03
n= once per year= 1
Want to quadruple amount, A=4P=4*$8000= $32,000
A=P(1+i/n)nt
$32,000=$8,000(1+0.03/1)1*t
*Use log laws to solve for t
32,000/8,000=(1.03)t
log(32,000/8,000)=log((1.03)t)
log(32,000/8,000)=t*log(1.03)
t= log(32,000/8,000)/log(1.03)
t= 46.9 years ( t in terms of year because interest is compounded once a year)
Check:
$32,000=$8,000(1+0.03/1)46.9
32,000=32,000.43 O.K