Question 761813: You just put $2193 in a CD that is expected to earn 17% compounded quarterly, and $7107 in a savings account that is expected to earn 3% compounded semiannually. Determine when, to the nearest year, the values of your two investments will be the same.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! You just put $2193 in a CD that is expected to earn 17% compounded quarterly, and $7107 in a savings account that is expected to earn 3% compounded semiannually. Determine when, to the nearest year, the values of your two investments will be the same.
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Compound interest formula: A=P(1+r/k)^kn, P=initial investment, r=annual interest rate, k=number of compounding periods, n=number of years, A=amount after n-years
For CD:
P=$2193
r/k=.17/4=0.0425
kn=4n
..
Savings account:
P=$7107
i=.03/4=0.015
kn=2n
..
2193(1+.0425)^4n=7107(1+.015)^2n
2193(1.0425)^4n=7107(1.015)^2n
2193/7107=1.015^2n/1.0425^4n
Take log of both sides
log(2193/7107)=2nlog(1.015)-4nlog(1.0425)
-0.5106=2n(.006466)-4n(.018076
-0.5106=2n(.006466-2(.018076)
-0.5106=2n(0.02968)
2n=.5106/.02968≈17.2
n≈8.6≈9yrs
Values of the two investments will be the same after about 9 years
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