Exploring Simple, Compound, and Continuous Interest

What is the primary goal of the mathematics of money series?

• To discuss only the economics of investments

• To promote financial products

• To explore the mathematical foundations of financial concepts

• To simplify financial concepts without deep mathematical insights

Why does the lender charge interest?

• Because it is a legal requirement

• To cover the risk of not being repaid

• To solely benefit from the borrower's hardship

• To increase their wealth without reason

What does 'P' represent in the simple interest formula?

• Period of the loan

• Principal amount of the loan

• Profit gained from the interest

• Percentage rate of the interest

How is compound interest different from simple interest?

• Compound interest accumulates interest on the initial principal only

• Compound interest accumulates interest on both the initial principal and accrued interest

• Compound interest only applies to long-term loans

• There is no difference; both are calculated in the same way

What does the 't' represent in the compound interest formula?

• Total interest accrued

• Time period in years

• Transaction number

• Total principal amount

What is the effect of increasing the number of compounding periods per year on the total amount owed?

• It increases the total amount owed

• It resets the interest rate to zero

• It has no effect on the total amount owed

• It decreases the total amount owed

What is the societal convention for expressing interest rates?

• Interest rates are shown as daily rates

• Interest rates are always shown as monthly rates

• Interest rates are expressed as annual rates

• There is no convention; rates are randomly expressed

What happens to the total amount owed when compounding is done continuously?

• It decreases over time

• It increases to a limit defined by e^(rt)

• It remains constant

• It becomes zero

What does continuously compounded interest imply about the frequency of compounding?

• Compounding occurs yearly

• Compounding occurs monthly

• Compounding occurs infinitely often

• Compounding occurs daily

Why is continuously compounded interest considered powerful in finance?

• It simplifies the calculation of interest

• It maximizes the growth of the invested amount

• It guarantees a fixed return rate

• It minimizes the risk of investment