Question

Maryann is planning a wedding anniversary gift of a trip to Hawaii for her husband at the end of 3 years. She will have enough to pay for the trip if she invests $2,500 per year until that anniversary and plans to make her first $2,500 investment on their first anniversary. Assume her investment earns a 4 percent interest rate, how much will she have saved for their trip if the interest is compounded in each of the following ways

Answer 1

Answer:

The answer is "She saves $\ 7804$ on the trip".

Explanation:

Please find the complete question in the attached file.

Given:

$(P) =\ 2500\\\\(n) =3 \ years\\\\(r) = 4\%\\\\ \text{compounding period in year}\ (m) =1$

The formula for Effective annual rate $= ((1+(\frac{r}{m}))^m)-1$

                                                                 $=((1+(\frac{4\%}{1}))^1)-1\\\\=((1+(\frac{4}{100}))^1)-1\\\\=((1+0.04)^1)-1\\\\=((1.04)^1)-1\\\\ =1.04-1\\\\ =0.04 \\\\ = 4\%$

Its potential value of its rental formula is used to measure the value of the rental at the middle of the 3rd year

 The formula for the future annuity $= P\times \frac{(((1+i)^n)-1)}{i}$

                                                         $=2500\times \frac{(((1+0.04)^3)-1)}{0.04}\\\\=2500\times \frac{(((1.04)^3)-1)}{0.04}\\\\=2500\times \frac{(1.124864-1)}{0.04}\\\\=2500\times \frac{0.124864}{0.04}\\\\=2500\times 3.1216\\\\=7804$