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

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

Step-by-step 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+((r)/(m)))^m)-1`

`=((1+((4\%)/(1)))^1)-1\\\\=((1+((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* ((((1+i)^n)-1))/(i)`

`=2500* ((((1+0.04)^3)-1))/(0.04)\\\\=2500* ((((1.04)^3)-1))/(0.04)\\\\=2500* ((1.124864-1))/(0.04)\\\\=2500* (0.124864)/(0.04)\\\\=2500* 3.1216\\\\=7804`