Question

In: Finance

You deposit $1,700 at the end of each year into an account paying 11.6 percent interest....

You deposit $1,700 at the end of each year into an account paying 11.6 percent interest.
Required:
(a) How much money will you have in the account in 17 years?
(b) How much will you have if you make deposits for 34 years?

Solutions

Expert Solution

Solution:
a. Money in account in 17 years   $ 80,030.06
Working Notes:
Notes: Here, we use concept of future value of annuity , to get the money in account after 17 years of annuity of $1,700 per year , in account which is paying 11.6 % per year.
Future value of annuity = P x ((1+i)^n - 1)/I
Where
P= Annual deposit per year =$1700 per year
i=annual interest rate = 11.6%
n= no. Of payments in a year x no. Of years = 1 x 17 =17
Now We get future value of annuity of 1700, in 17 years
Future value of annuity = P x ((1+i)^n - 1)/i
Future value of annuity = $1700 x ((1+ 11.6%)^17 - 1)/11.6%
Future value of annuity =80,030.05801
Future value of annuity in 17 years =80,030.06
b. Money in account in 34 years   $ 597,094.22
Working Notes:
Notes: Here, we use concept of future value of annuity , to get the money in account after 34 years of annuity of $1,700 per year , in account which is paying 11.6 % per year.
Future value of annuity = P x ((1+i)^n - 1)/i
Where
P= Annual deposit per year =$1700 per year
i=annual interest rate = 11.6%
n= no. Of payments in a year x no. Of years = 1 x 34 =34
Now We get future value of annuity of 1700, in 34 years
Future value of annuity = P x ((1+i)^n - 1)/i
Future value of annuity = $1700 x ((1+ 11.6%)^34 - 1)/11.6%
Future value of annuity =597,094.2227035
Future value of annuity in 34 years =597,094.22
Please feel free to ask if anything about above solution in comment section of the question.

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