Question

​Recently, More Money 4U offered an annuity that pays 6.0 % compounded monthly. If $1,828 is deposited into this annuity every​ month, how much is in the account after 11 ​years? How much of this is​ interest?

Type the amount in the​ account: ​(Round to the nearest​ dollar.)

Type the amount of interest​ earned: ​(Round to the nearest​ dollar.)

Answer 1

annuity is two types

when the payments are made at beginning of the each month then it is called annuity due

when the payments are made at end of the each month then it is called ordinary annuity

so let us find the annuity due first.

annuity due

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 = $1828

        r = rate of interest = 6% = 6/100 = 0.06

       Here compounding frequency is monthly so r = 0.06 / 12 = 0.005

       n = Number of payments = 11 x 12 = 132

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

FV = 1828 X [[(1+0.005)¹³²-1] / (0.005)](1+0.005)

FV = 1828 X [[(1.005)¹³²-1] / (0.005)](1.005)

FV = 1828 X [[1.9316-1] / (0.005)](1.005)

FV = 1828 X [[0.9316] / (0.005](1.005)

FV = 1828 X [ 186.322 ] (1.005)

FV = 1828 X 187.25361

FV = 342299.599 ~ 342299.6

So the future value for 11 years is $ 342299.6

Now the total deposit amount = C x n = 1828 x 132

                                                                          =$241296

Now the interest amount = FV – total deposit = 342299.6 – 241296 = $101003.6

Total interest earned = $101003.6

Ordinary Annuity

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

FV = C x [ ( 1 + r )ⁿ-1 ] / ( r )

Here FV = future value = ?

        C = Cash flow per period = $1828

        r = rate of interest = 6% = 6/100 = 0.06

       compounded monthly so r = 0.06/12 = 0.005

       n = Number of payments = 11 x 12 = 132

FV = 1828 x [ ( 1 + 0.005 )¹³² – 1 ] / (0.005)

FV = 1828 x [ ( 1 .005 )¹³² – 1 ] / (0.005)

FV = 1828 x [ (1.9316- 1)] / (0.005)

FV = 1828 x 0.9316 / (0.005)

FV = 1828 x 186.32

FV = 340592.96

So Future value after 11 years = $340592.96

Now the total deposit amount = C x n = 1828 x 132

                                                                          =$241296

Now the interest amount = FV – total deposit = 340592.96 – 241296 = $99296.96

Total interest earned = $99296.96