Question

Not homework just review for test not worth any points

Answer 1

Recall that:

Interest is the monetary gain for lending money to a third party.

Simple interest is applying the interest to the original amount without considering the extra flow of money each time the interest is applied.

Compounded interest is applying the interest to the total amount including the extra flow of money each time the interest is applied.

1) Plan A. From the given information, in 12 months Ari will earn:

`I=500\cdot0.065\cdot12=390.`

dollars, therefore she will have a total of $890.00.

2) Plan B. Now we use the formula for compounded interest to compute the total amount that Ari will have after one year:

`A=500(1+0.065)^(12)=500\cdot2.129096\approx1064.55.`

3) From the above calculations, we conclude that Ari will make more money if she invests in plan B.

4) Ari has to leave the money for another:

Using plan B. Let t be the number of extra months Ari needs to leave the money in the fund, then:

`1100=500\cdot(1.065)^(12+t)\text{.}`

Solving for t, we get:

`\begin{gathered} 1.065^(12+t)=2.2, \\ (12+t)ln(1.065)=\ln (2.2), \\ 12+t=(\ln (2.2))/(\ln (1.065))=12.52, \\ t=12.52-12=0.52. \end{gathered}`

Then, Ari needs to leave the money for another half a month but since the interest is applied each month she needs to leave the money for another whole month.

Using Plan A: Let t be the number of extra months Ari needs to leave the money in the fund, then:

`1100=500\cdot0.065\cdot(12+t)\text{ +500.}`

Solving for t we get:

`\begin{gathered} (1100-500)/(500\cdot0.065)=12+t, \\ t=(600)/(32.5)-12, \\ t=6.46. \end{gathered}`

Then, Ari needs to leave the money for another 6.46 months but since the interest is applied monthly she needs to leave the money for another 7 months.