Money Talk
Pain or Gain
Formula Factory
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100
What does the principal represent in a compound interest formula?
The starting amount of money before any interest is added.
100
If money grows by a fixed percent each year, is the growth additive or multiplicative?
Multiplicative
100
What is the general form of a compound interest formula for annual compounding?
100
Two accounts compound interest at the same frequency but have different interest rates. Which is better long term?
The account with the higher interest rate.
100
A student says compound interest adds the same amount every year.
Compound interest adds a different amount each year because the balance changes.
200
What does the interest rate describe?
The percent change in the balance per year.
200
How is the growth factor related to the interest rate?
The growth factor is one plus the interest rate (written as a decimal).
200
Which part of the compound interest formula represents the starting amount?
P (Principal)
200
Two accounts have the same starting amount and interest rate. One compounds more frequently. Which grows more?
The account that compounds more frequently.
200
A student uses the interest rate instead of the growth factor in the formula.
Add 1 to the interest rate to get the growth factor.
300
What does it mean when interest is compounded?
Interest is earned on both the original amount and the interest already added.
300
Declan is calculating the interest on a loan that is compounded monthly at 18%. What growth factor should he use per month?
This means the balance is multiplied by 1.015 each month.
300
Write the compound interest formula when interest is compounded multiple times per year.
300
Two accounts start with the same amount. One earns simple interest of 7% and one earns compound interest of 6%. Which grows faster?
The one that earns compound interest.
300
A student says a negative time value means the money is negative.
It represents a time before the starting point.
400
In a compound interest model, what does the variable exponent measure?
The number of times interest in compounded/calculated.
400
Why is the growth factor always greater than 1 for compound interest?
Because the balance is increasing, not decreasing. It includes the amount already in the account.
400
What does the variable n or m represent in a compound interest formula?
The number of times interest is compounded each year.
400
Why does compound interest become more powerful over longer time periods?
Because interest is repeatedly earned on an increasing balance.
400
Tim is calculating how much he owes Marcus on a loan that is compounded quarterly at 8% for 3 years. He uses a factor of 1.02 and an exponent of 3.
The exponent should be the total number of quarters: 4×3=12
500
Explain the difference between simple interest and compound interest.
Simple interest is earned only on the starting amount, while compound interest is earned on the starting amount and previously earned interest.
500
Two accounts start with the same amount. One grows with compound interest and one increases by a fixed amount each year. Which will be larger after many years, and why?
The compound interest account, because multiplicative growth eventually outpaces additive growth.
500
Why does the exponent include both time and compounding frequency?
Because interest is applied once for every compounding period over the total time.
500
Why is compound interest often called “interest on interest”?
Because new interest is calculated on both the original money and previously earned interest.
500
Why are compound interest models not reasonable forever in real life?
Because real-world limits like resources, income, and policies prevent unlimited growth.