alexlawyer
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Lily wants to buy a new computer which costs 4000$, but does not have enough money to pay for it immediately. Her parents find a store that offers a payment plan that requires an initial payment of 1500$ immediately, and then 2750$ after 1 year.

1)What is the implied yearly interest rate?
2)What is the implied monthly compound interest rate?

I'm an international student and I'm struggling with this type of questions.
I'm doing similar to A-level Maths and I'm not used to these questions. These resemble Economics questions in my curriculum.

4000-1500=2500$ amount of money which is assumed to be "borrowed"

2750-2500=250$ amount of money which is received by the store as interest.
p is the interest rate
p/100 * 2500=250
p=250/2500*100 => p=10% yearly interest rate

Am I doing it right?

..And the second question
Why are they asking about monthly compound interest rate if they specify in the question that she pays the rest after 1 year?
How can I solve this?
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gdunne42
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(Original post by alexlawyer)
Lily wants to buy a new computer which costs 4000$, but does not have enough money to pay for it immediately. Her parents find a store that offers a payment plan that requires an initial payment of 1500$ immediately, and then 2750$ after 1 year.

1)What is the implied yearly interest rate?
2)What is the implied monthly compound interest rate?

I'm an international student and I'm struggling with this type of questions.
I'm doing similar to A-level Maths and I'm not used to these questions. These resemble Economics questions in my curriculum.

4000-1500=2500$ amount of money which is assumed to be "borrowed"

2750-2500=250$ amount of money which is received by the store as interest.
p is the interest rate
p/100 * 2500=250
p=250/2500*100 => p=10% yearly interest rate

Am I doing it right?

..And the second question
Why are they asking about monthly compound interest rate if they specify in the question that she pays the rest after 1 year?
How can I solve this?
Your thought process is fine and part a is correct.

I don't know if you have learned to use multipliers for % calculations
E.g. To add 20% to a price the multiplier would be x 1.2 to add 1% it would be x 1.01
For part a, using the letter M for the multiplier
2500 x M = 2750
Therefore M = 2750/2500 = 1.1 and the annual increase is 10%

For compound interest you apply the multiplier each time interest is added.
E.g. If you invest $100 at 2% compound for 4 years
100 x 1.02 x 1.02 x 1.02 x 1.02
or 100 x 1.02^4

In part b since there are 12 months in the year
2500 x M^12 = 2750
M^12= 1.1, your calculator can tell you what M is and hence the monthly compound interest rate.


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alexlawyer
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Thank you very much for your help!!
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alexlawyer
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(Original post by gdunne42)
Your thought process is fine and part a is correct.

I don't know if you have learned to use multipliers for % calculations
E.g. To add 20% to a price the multiplier would be x 1.2 to add 1% it would be x 1.01
For part a, using the letter M for the multiplier
2500 x M = 2750
Therefore M = 2750/2500 = 1.1 and the annual increase is 10%

For compound interest you apply the multiplier each time interest is added.
E.g. If you invest $100 at 2% compound for 4 years
100 x 1.02 x 1.02 x 1.02 x 1.02
or 100 x 1.02^4

In part b since there are 12 months in the year
2500 x M^12 = 2750
M^12= 1.1, your calculator can tell you what M is and hence the monthly compound interest rate.


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Effective rate for period = (1 + annual rate)^(1 / # of periods) – 1
What about this equation? found it online..
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