Question

Ashley has a large and growing collection of animated movies. She wants to replace her old television with a new LCD model, so she has started saving for it. At the end of each year, she deposits $1,060 in her bank account, which pays her 12% interest annually. Ashley wants to keep saving for three years and then buy the newest LCD model that is available. Ashley’s savings are an example of an annuity. How much money will Ashley have to buy a new LCD TV at the end of three years? $3,040.33 $4,006.09 $2,545.94 $3,576.86 If Ashley deposits the money at the beginning of every year and everything else remains the same, she will save by the end of three years.

Answer 1

Answer:

Option (D) is correct.

Explanation:

1.We use the formula:

$A=P(1+\frac{r}{100})^{n}$

where

A=future value

P=present value

r=rate of interest

n=time period.

$A=1,060(1.12)^{2}+ 1,060(1.12)^{1} + 1,060$

$A=1,060[(1.12)^{2}+(1.12)^{1} + 1]$

         = 1,060 [1.2544 + 1.12 + 1]

         = 1,060 × 3.3744

         = $3,576.864

Therefore, the amount of $3,576.864 will Ashley have to buy a new LCD TV at the end of three years.

(b) Future value of annuity due = Future value of annuity × (1 + interest rate)

                                                    = $3,576.86(1 + 0.12)

                                                    = $3,576.86 × 1.12

                                                    = $4,006.08

She will save around $4,006.08