Compare borrowing options using interest rates and fees

Borrowing options are compared by relating the principal, interest rate, time, compounding period, repayment amount, and fixed or transaction fees to the total cost of credit over a common term. The mathematics includes percent calculations and simple or periodically compounded interest when specified, emphasizing that a lower advertised rate may still produce a higher overall cost once fees and compounding are included. Detailed amortization schedules, variable rates, continuously compounded interest, and complex penalties are beyond this scope.

Detailed Explanation: Compare borrowing options using interest rates and fees

To compare borrowing options fairly, use the same principal and the same borrowing time for each option. Find:

The interest charged
Any fixed or transaction fees
The total repayment amount
The total cost of credit, which is interest plus fees

A lower advertised interest rate does not always mean a lower total cost.

Example: You need to borrow 1{,}000$ for 1 year.

Option A: $8\%$ simple interest and a 30$ fee
Option B: $6\%$ interest compounded monthly and a 70$ fee

Step 1: Calculate Option A

For simple interest, use

I=Prt

where:

$P$ is the principal,
$r$ is the annual interest rate as a decimal,
$t$ is the time in years.

For Option A:

I=(1000)(0.08)(1)=80

The interest is 80$.

Add the fee to find the total cost of credit:

\text{Total cost}=\$80+\$30=\$110

The total repayment is:

\$1{,}000+\$110=\$1{,}110

Step 2: Calculate Option B

For interest compounded monthly, use

A=P\left(1+\frac{r}{n}\right)^{nt}

where:

$A$ is the amount owed before fees,
$n$ is the number of compounding periods per year.

For Option B, $n=12$ :

A=1000\left(1+\frac{0.06}{12}\right)^{12(1)}

A=1000(1.005)^{12}\approx \$1{,}061.68

The interest is:

\$1{,}061.68-\$1{,}000=\$61.68

Now add the 70$ fee:

\text{Total cost}=\$61.68+\$70=\$131.68

The total repayment is:

\$1{,}000+\$131.68=\$1{,}131.68

Step 3: Compare the options

Option	Interest	Fees	Total cost of credit	Total repayment
A	80.00$	30.00$	110.00$	1{,}110.00$
B	61.68$	70.00$	131.68$	1{,}131.68$

Option B advertises the lower interest rate, but it has the higher fee. Therefore, Option A is cheaper overall by 21.68$:

\$131.68-\$110.00=\$21.68

Always compare the total cost of credit, not just the advertised interest rate.

Learn by doing: Compare borrowing options using interest rates and fees

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Financial Literacy - Interest and Fees - Compound Discrete - Comparison With Fees to Better Option

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