She should invest [tex]\$ 12181.25[/tex] now at [tex]7\%[/tex], compounded quarterly, so that she have enough to buy a new car.
What is Compound interest?
Compound interest is an interest which is earned on the principal and the interest together over a given time period.
We have, for Compound interest,
Amount [tex]= P(1+\frac{R}{100} )^t[/tex]
Also,
Amount [tex]=[/tex] Principal + Interest
We have,
Amount [tex]= \$ 15000[/tex]
Rate of Interest [tex]=7 \%[/tex]
Time period [tex]= 3[/tex] years
As compounded quarterly, then
Rate [tex]= \frac{7}{4}\%[/tex]
Time [tex]=3*4=12[/tex] years
Now,
[tex]15000 = P(1+\frac{7}{400} )^{12}[/tex]
[tex]15000=P(1.2314)[/tex]
[tex]P= \$ 12181.25[/tex]
Hence, we can say that she should invest [tex]\$ 12181.25[/tex] now at [tex]7 \%[/tex], compounded quarterly, so that she have enough to buy a new car.
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