Question

compound interest — step - by - step student worksheet
what youll need: scientific calculator, ability to convert percents to decimals, and comfort with logarithms.
formula: $a = pcdot(1+\frac{r}{n})^{nt}$ where:

• $a$ = the future amount (principal + interest)
• $p$ = the principal (starting amount today)
• $r$ = the annual nominal interest rate (as a decimal, so 6%→0.06)
• $n$ = the number of compounding periods per year (e.g., 1 = annual, 2 = semiannual, 4 = quarterly, 12 = monthly, 365 = daily)
• $t$ = the number of years invested (can be fractional, like 1.5 years = 18 months)

warm - up (foundations)

1. convert each percent to a decimal: 6%, 4.5%, 7.2%, 2.2%

answer space:

1. match the compounding term to $n$: annually, semiannually, quarterly, monthly, daily (365).

answer space: $n$ = 1, 2, 4, 12, 365

1. circle the correct variable for each meaning:

• amount today (principal): a / p / r
• number of compounds per year: p / n / t
• years invested: a / r / t

1. simple vs. compound (no calculation): which usually grows money faster over multiple years—simple or compound interest? why?

Explanation:

Step1: Convert percentages to decimals

To convert a percentage to a decimal, divide by 100. So, 4.5% = 4.5/100 = 0.045, 7.2%=7.2/100 = 0.072, 2.2%=2.2/100 = 0.022.

Step2: Match compounding terms to n

The given matches are correct as per the definitions of compounding periods.

Step3: Identify variables

The amount today (principal) is $P$. The number of compounds per year is $n$. The years invested is $t$.

Step4: Compare simple and compound interest

Compound interest usually grows money faster over multiple years because in compound - interest, interest is earned on both the principal and the accumulated interest from previous periods, while in simple interest, interest is only earned on the principal amount.

Answer:

1. 0.045, 0.072, 0.022
2. Correct as marked: $n = 1,2,4,12,365$
3. amount today (principal): $P$; number of compounds per year: $n$; years invested: $t$
4. Compound interest grows money faster over multiple years because interest is earned on principal and accumulated interest.