Question

21. the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the required payment for the sinking fund. (Round your answer to the nearest cent.)

Monthly deposits earning 4% to accumulate $3000 after 10 years.

22. the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the required payment for the sinking fund. (Round your answer to the nearest cent.)

Yearly deposits earning 12.9% to accumulate $2500 after 12 years.

Answer 1

Ordinary Annuity

According to given information man deposits the amount at the end of each semi month so it will be an ordinary annuity payments.

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

FV = C x [ ( 1 + r )ⁿ-1 ] / ( r )

Here FV =  future value = $3000

        C = Cash flow per period  =  ?

        r = rate of interest = 4% = 4/100 = 0.04

       compounded monthly   so  r  = 0.04/12  = 0.003333

       n = Number of payments  = 10 years so 10 x 12 = 120

3000 = C x [ ( 1 + 0.003333 )¹²⁰ – 1 ] / (0.003333)

3000 =C X  [ ( 1 .003333 )¹²⁰ – 1 ] / (0.003333)

3000 = C X [ 1.4907 – 1 ] / (0.003333)

3000 = C X [ 0.4907 ] / (0.003333)

3000 = C X ( 147.2247 )

C =  3000 / 147.2247 = 20.37

So the monthly payment = $20.37

Ordinary Annuity

According to given information man deposits the amount at the end of each semi month so it will be an ordinary annuity payments.

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

FV = C x [ ( 1 + r )ⁿ-1 ] / ( r )

Here FV =  future value = $2500

        C = Cash flow per period  =  ?

        r = rate of interest = 12.9% = 12.9/100 = 0.129

       compounded monthly   so  r  = 0.129/12  = 0.01075

       n = Number of payments  = 12 years so 12 x 12 = 144

2500 = C x [ ( 1 + 0.01075 )¹⁴⁴ – 1 ] / (0.01075)

2500 =C X  [ ( 1 .01075 )¹⁴⁴ – 1 ] / (0.01075)

2500 = C X [ 4.6633 – 1 ] / (0.01075)

2500 = C X [ 3.6633 ] / (0.01075)

2500 = C X ( 340.772 )

C =  2500 / 242.586  = 7.34

So the monthly payment = $7.34