calculating the number of payments.ppt

Chapter 11: Ordinary Annuities: Payment Size, Term, and Interest Rate
calculating the number of payments
1
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.
2
Calculating the number of payments
Ordinary annuities
Algebraic method
3
Step 1: calculate the periodic interest rate per payment
step 2:
FV
PV
n
1/y
PMT
results
FV
PV
n
1/y
PMT
R
p
p
R
0
0
FV
PV
Final lump
payment
Initial
lump
payment
Financial calculator method
results
CPT
CPT
4
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?
5
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.
6
R=$220 An=$20,000
j=12% compounded monthly
i=p=j/m=1% per month
Solution:
FV
PV
n
i
PMT

220
1
0
20,000
+/-
It will take 241
payments, requiring
20 years and 1 month,
to pay off the loan.
The last payment will
be slightly less than
$220.
Question a:
7
b, R=$220+$20=$240 An=$20,000
i=p=j/m=1% per month
n
PMT

220
+/-
It will take 181 months (15 years and 1 month) to
pay off the loan. The last payment will be
approximately *($240)=$17.
Question b:
8
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,