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4) (Related to Checkpoint 6
4) (Related to Checkpoint 6.1) (Annuity payments) Mr. Bill S. Preston, Esq., purchased a new house for $80,000. He paid $15,000 upfront and agreed to pay the rest over the next 10 years in 10 equal annual payments that include principal payments plus 15 percent compound interest on the unpaid balance. What will these equal payments be? a. Mr. Bill S. Preston, Esq., purchased a new house for $80,000 and paid $15,000 upfront. How much does he need to borrow to purchase the house? (Round to the nearest dollar.) b. If Bill agrees to pay the loan over the next 10 years in 10 equal end-of-year payments plus 15 percent compound interest on the unpaid balance, what will these equal payments be? (Round to the nearest cent.)
5. (Annuity payments) To pay for your child's education, you wish to have accumulated $16,000 at the end of 9 years. To do this, you plan to deposit an equal amount into the bank at the end of each year. If the bank is willing to pay 8 percent compounded annually, how much must you deposit each year to obtain your goal? The amount of money you must deposit each year in order to obtain your goal is $ (Round to the nearest cent.)
Expert Solution
| The present value of the payment to be paid equally in 10 annual installments (ie. Annuities) is |
| 80000-15000= 65000 |
| the interest rate is 15% or 0.15 p.a. |
| To find that equal pmt,--- We will use the formula,to find the PV of ordinary annuity-- |
| PVOA=Pmt.*(1-(1+r)^-n)/r |
| where, we have, the PVOA as $ 65000 |
| Pmt.---- is the equal pmt. amt. to be found out---?? |
| r= annual rate of interest, ie. 15% or 0.15 p.a. |
| n= no.of pmts.--- 10 |
| now, plugging these values in the formula, |
| 65000=Pmt.*(1-1.15^-10)/0.15 |
| so, the Pmt.=65000/((1-1.15^-10)/0.15) |
| 12951.38406 |
| so, the answers will be: |
| a. He need to borrow $ 65000 |
| b.The 10 equal payments will be $ 12951. 38 each |
| 5. The amount of money you must deposit each year to obtain your goal |
| can be found by using the future value of ordinary annuity formula, |
| FVOA=Pmt.*((1+r)^n-1)/r |
| where, we have, the FVOA at end of 9 yrs.as $ 16000 |
| Pmt.---- is the equal amt. to be deposited at end of each yr. ---to be found out---?? |
| r= annual rate of interest, ie. 8% or 0.08 p.a. |
| n= no.of deposits --- 9 |
| now, plugging these values in the formula, |
| 16000=Pmt.*((1+0.08)^9-1)/0.08= |
| Pmt.=16000/((1.08^9-1)/0.08)= |
| 1281.28 |
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