Question

After carefully exmaining your​ budget, you determine you can manage to set aside ​$370 per year. You set up an annuity due of ​$370 annually at 6.5 ​% annual interest. How much will you have contributed after 22 ​years? What is the future value of the annuity after 22 ​years? How much interest will the annuity have​ earned?

Answer 1

the future value of the annuity is $17057.60

interest is $8917.60

Explanation:

Given data

annuity = $370

rate (r) = 6.5% = 0.065

time period (t)= 22 years

to find out

the future value of the annuity and interest

solution

we know the future value of the annuity formula that is given below

future value = annuity× (
`(1+r)^(t)` -1 / r ) ..................1

so now put all value annuity, rate , time in equation 1 to find out future value

future value = annuity× (
`(1+r)^(t)` -1 / r )

future value = 370 × (
`(1+0.065)^(22)` -1 / 0.065 )

future value = 370 × 46.101636

future value = 17057.60532

so the future value of the annuity is $17057.60

and interest = future value - annuity for 22 year

interest = 17057.60 - (22× 370)

interest = 17057.60 - (8140)

interest = 8917.60

so interest is $8917.60