Question

14.1.19 Find the future value of an annuity due with an annual payment of ​$11 comma 000 for three years at 3​% annual interest using the simple interest formula. How much was​ invested? How much interest was​ earned? What is the future value of the​ annuity? ​$ nothing ​(Round to the nearest cent as​ needed.) Enter your answer in the answer box and then click Check Answer. 2 parts remaining

New problem 14.1.23 Find the future value of a quarterly annuity due of ​$4 comma 100 for five years at 10​% annual interest compounded quarterly. How much was​ invested? How much interest was​ earned? LOADING... Click the icon to view the Future Value of​ $1.00 Ordinary Annuity table. The future value is ​$ nothing.​ (Round to the nearest cent as​ needed.) Enter your answer in the answer box and then click Check Answer. 1 part remaining

Answer 1

annuity due

According to given information the deposits amount at the beginning of each year so it will be an annuity due payments.

We can use the formula for finding the future value as below

FV = C x [[ ( 1 + r )ⁿ-1 ] / ( r )](1+r)

Here FV =  future value = $?

        C = Cash flow per period  =  $11000

        r = rate of interest = 3% = 3/100 = 0.03

       Here compounding frequency is annually  so r = 0.03

       n = Number of payments = 3

       FV = C x [[ ( 1 + r )ⁿ-1 ] / ( r )](1+r)

FV = 11000 X [[(1+0.03)³-1] / (0.03)](1+0.03)

FV = 11000 X [[(1.03)³-1] / (0.03)](1.03)

FV = 11000 X [[1.092727-1] / (0.03)](1.03)

FV = 11000 X [[0.092727] / (0.03](1.03)

FV = 11000 X [ 3.0909 ] (1.03)

FV = 11000 X 3.183627

FV = 35019.897 ~ 35020

So the future value for 3 years is $ 35020

Total deposit amount =  C x number of payments = 11000 x 3 = $33000

Total interest earned = FV – deposit amount = 35020 – 33000 = $2020

We can use the formula for finding the future value as below

FV = C x [[ ( 1 + r )ⁿ-1 ] / ( r )](1+r)

Here FV =  future value = $?

        C = Cash flow per period  =  $4100

        r = rate of interest = 10% = 10/100 = 0.1

       Here compounding frequency is quarterly  so r = 0.1/4 = 0.025

       n = Number of payments = 5 x4 = 20

       FV = C x [[ ( 1 + r )ⁿ-1 ] / ( r )](1+r)

FV = 4100 X [[(1+0.025)²⁰-1] / (0.025)](1+0.025)

FV = 4100 X [[(1.025)²⁰-1] / (0.025)](1.025)

FV = 4100 X [[1.6386-1] / (0.025)](1.025)

FV = 4100 X [[0.6386] / (0.025](1.025)

FV = 4100 X [ 25.5446 ] (1.025)

FV = 4100 X 26.1832

FV = 107351.4236 ~ 107351.5

So the future value for 5 years is $ 107351.5

Total deposit amount =  C x number of payments = 4100 x 20 = $82000

Total interest earned = FV – deposit amount = 107351.5 – 82000 = $25351.5