Question

This assignment covers the material in: 2.1 Simple Interest 2.2 Compound Interest 2.3 Annuities 2.4 Amortization

20A. n 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 accumulated amount of the annuity. (Round your answer to the nearest cent.)

$1000 monthly at 5.5% for 20 years. _______$

20B.In 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 $9000 after 10 years.______$

20C. In 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 $8500 after 12 years.______$

Answer 1

Solution 20A:

Monthly interest rate = 5.5%/12= 0.45833%

Period = 20*12 = 240 monthly period

Monthly annuity = $1,000

Accumulated amount of annuity = $1,000 * Cumulative FV factor at 0.45833% for 240 periods

= $1,000 * 435.62740 = $435,627.40

Solution 2B:

Monthly interest rate = 4%/12 = 0.333333%

Periods = 10*12 = 120 monthly periods

Accumulated amount = $9,000

Let monthly deposit = P

P * Cumulative FV factor at 0.333333333% for 120 periods = $9,000

P * 147.2498 = $9,000

P = $61.12

Therefore monthly deposit amount = $61.12

Solution 20C:

Interest rate = 12.9%

Accumulated amount = $8,500

Period = 12 years

Let yearly deposit = P

P * Cumulative FV factor at 12.9% for 12 periods = $8,500

P * 25.49392 = $8,500

P = $333.41

Monthly Deposit amount = $333.41