Question

1. 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 12.8% to accumulate $3500 after 12 years.

2. 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 amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.)

$245 monthly at 5.5% to accumulate $25,000.

__________yr

Answer 1

Q1. This is an example of an ordinary annuity, where yearly payments are made for 12 years to accumulate $3,500 at 12.8%. We need to calculate the amount of annual payment made.

Mathematical relation for FV of annuity is:

Substituting values in this relation, we get:

3500 = P * 25.3387

P = $138.13 --> Annual payment required

Q2. In this case, we need to calculate the number of months required to accumulate $25,000, by depositing $245 monthly at 5.5% rate.

r = 5.5%/12 = 0.4583% (monthly)

n = 0.3837/0.004573 = 83.91 months

Number of years = 83.91 months /12 = 6.99 years