nuffield free-standing mathematics activity annual percentage rate with more than one instalment
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Nuffield Free-Standing Mathematics Activity Annual percentage rate with more than one instalment. Lower APR. APR with more than one instalment. It’s a bargain! A few easy instalments. Is this APR really correct?. This activity is about finding and checking APRs. - PowerPoint PPT PresentationTRANSCRIPT
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© Nuffield Foundation 2011
Nuffield Free-Standing Mathematics Activity
Annual percentage rate with more than one instalment
Lower APR
![Page 2: Nuffield Free-Standing Mathematics Activity Annual percentage rate with more than one instalment](https://reader034.vdocuments.us/reader034/viewer/2022042616/56813063550346895d963490/html5/thumbnails/2.jpg)
It’s a bargain!
A few easy instalments.
Is this APR really correct?
APR with more than one instalment
This activity is about finding and checking APRs
![Page 3: Nuffield Free-Standing Mathematics Activity Annual percentage rate with more than one instalment](https://reader034.vdocuments.us/reader034/viewer/2022042616/56813063550346895d963490/html5/thumbnails/3.jpg)
For one instalment the loan is:
C = which gives the APR, i, as a decimal when a loan of £C is paid back by a single repayment £A after n years.
APR with more than one instalment
The general APR formula for cases involving more than one instalment is C =
m
ki
kA
kt1)1(
where i is the APR expressed as a decimal
ni1A
k is the number identifying a particular instalment
Ak is the amount of the instalment k
tk is the interval in years between the payment of the instalment and the start of the loan
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When there are 4 annual instalments, A1, A2, A3 and A4 , the formula becomes
432 14
13
12
11
i
A
i
A
i
Ai
AC
Think aboutWhat is the formula for 3 annual instalments?
APR with more than one instalment
What is the formula for 5 annual instalments?
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Reflect on your workWhy is it important to know the APR when a loan is repaid in several instalments?
What methods do you know for calculating the APR?
How would you set up a spreadsheet to carry out the calculations required by the interval bisection method?
APR with more than one instalment
Write down the formulae used when there is: 1 repayment, 2 repayments, and 3 repayments.