calculating the number of payments参考.ppt

Chapter 11: Ordinary Annuities: Payment Size, Term, and Interest Rate 11.2 calculating the number of payments Sometimes we need calculate the number of payments of an annuity. Determining the time required for periodic payments to pay off a loan. Determining the time required for a periodic savings plan to reach a savings goal. Determining how long an annuity purchased with a lump investment will deliver a specified payment. Calculating the number of payments Step 1: calculate the periodic interest rate per payment step 2: Example Roy and Lynn are discussing the terms of a $20,000 home improvement loan with their bank’s lending officer. The interest rate on the loan will be 12% compounded monthly. a, how long will it take to repay the loan if the monthly payments are $220? b, how long will it take to repay the loan if Roy and Lynn pay an extra $20 per month? c, calculate the approximate total of the (nominal) interest savings over the life of the loan as a result of making payments of $240 instead of $220 per month. R=$220 An=$20,000 j=12% compounded monthly i=p=j/m=1% per month b, R=$220+$20=$240 An=$20,000 i=p=j/m=1% per month If the monthly payment is $220, n=241 the total of all payments=241*$220=$53,020 the nominal interest =$53,020-$20,000=$33,020 If the monthly payment is $240, n=180 the total of all payments=180*$240=$43,200 the nominal interest =$43,200-$20,000=$23,200 Example a, Annual contributions of $5000 will be made at every year-end to an RRSP. To the nearest year, how long will it take for the funds in the RRSP to grow to $500,000 if they earn7.5% compounded annually? b, If the $500,000 will be used purchase an annuity earning 8% compounded quarterly and paying $12,000 at the end of each quarter, how long after the purchase date will the annuity payments continue? R=$5000 j=7.5% compounded annually payment interval=1 year p=i=j/m=7.5% per year Sn=$500,000 j=8% compounded quarterly An=$500,000 payment interval