1. Starting on his 26th birthday, Fred deposits $3000 a year into a savings fund. His last deposit is at the age of 45. Starting 1 year later, he makes annual withdrawals for 20 years. If j_1=10%. throughout, find the size of these annual withdrawals? *
2. A parcel of land valued at $35,000 is sold for $10,000 down. The buyer agrees to pay the balance with interest at j12=12% by paying $600 monthly as long as necessary, the first payment due one year from now. Find the number of $600 payments needed and the size of concluding payment one month after the last $600 payment. *

1.     19,830.12 
2. 54 payments

Notes:

• We use ordinary annuity when there is a time lapse between the subject year or month and the year or month of first payment. When the periodic cash flow is immediate, then we use annuity due
• In the first problem we have to compute for the future value of the annual deposits for 19 years that will cover the 20 years of withdrawals. Hence the future value of annual deposits is equal to the present value at year 19 of the annual withdrawals. Note that we use formula for future value of annuity due since the first deposit is done immediately at the age of 26 (year 0). After computing this, it will also be the present valur of annual deposits for twenty years. This time we will use the formula for present value of ordinary annuity as there is a one year gap from the last deposit to the first withdrawal.
• In the second problem, we discount the first 600 payment at the whole rate of 12 percent since there is a 1 year gap between the first payment of 600 and the payment of 10,000. Then we will discount the rest using 1% rate (12%/12) as the payment will be done monthly. To identify the number of payments, we have to compute first the factor. so we deduct the discounted value of 600 from 25,000 and divide the result by 600. We will get the factor, Using the table for PV of ordinary annuity under 1%, we can determine that the factor is after 52 and before 53. We will use 53 and use this factor to multiply to 600. We deduct the result to the remaining balance to get the concluding payment. Then we add the 53 payments to the first payment, we get a total of 54 payments of 600.

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