Worksheet on compound interest calculations with various investment and loan scenarios.

Here are the step-by-step solutions for each problem on your worksheet. I have calculated them carefully using the compound interest formula:

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

Where:
* $A$ = Total amount (final answer)
* $P$ = Principal (starting money)
* $r$ = Annual interest rate (as a decimal)
* $n$ = Number of times compounded per year
* $t$ = Time in years

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1.) Your 3 year investment of $\$20,000$ received $5.2\%$ interest compounded semi-annually. What is your total return?

* $P = 20,000$
* $r = 0.052$
* $n = 2$ (semi-annually means twice a year)
* $t = 3$

Calculation:
$$A = 20,000(1 + \frac{0.052}{2})^{(2 \times 3)}$$
$$A = 20,000(1 + 0.026)^6$$
$$A = 20,000(1.026)^6$$
$$A = 20,000(1.166498...)$$
$$A \approx 23,329.97$$

Answer: $\$23,329.97$

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2.) You borrowed $\$59,000$ for 2 years at $11\%$ which was compounded annually. What total will you pay back?

* $P = 59,000$
* $r = 0.11$
* $n = 1$ (annually means once a year)
* $t = 2$

Calculation:
$$A = 59,000(1 + \frac{0.11}{1})^{(1 \times 2)}$$
$$A = 59,000(1.11)^2$$
$$A = 59,000(1.2321)$$
$$A = 72,693.90$$

Answer: $\$72,693.90$

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3.) Your allowance of $\$190$ got $11\%$ compounded monthly for $1 \frac{2}{3}$ years. What's it worth after the $1 \frac{2}{3}$ years?

* $P = 190$
* $r = 0.11$
* $n = 12$ (monthly)
* $t = 1 \frac{2}{3}$ years. To make this easier for the calculator, convert to months or improper fraction. $1 \frac{2}{3} = \frac{5}{3}$.
* Total periods ($n \times t$) = $12 \times \frac{5}{3} = 20$ months.

Calculation:
$$A = 190(1 + \frac{0.11}{12})^{20}$$
$$A = 190(1 + 0.009166...)^{20}$$
$$A = 190(1.009166...)^{20}$$
$$A = 190(1.20026...)$$
$$A \approx 228.05$$

Answer: $\$228.05$

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4.) Your $6 \frac{1}{4}$ year investment of $\$40,000$ at $14\%$ compounded quarterly is worth how much now?

* $P = 40,000$
* $r = 0.14$
* $n = 4$ (quarterly)
* $t = 6.25$ ($6 \frac{1}{4}$ as a decimal)
* Total periods ($n \times t$) = $4 \times 6.25 = 25$.

Calculation:
$$A = 40,000(1 + \frac{0.14}{4})^{25}$$
$$A = 40,000(1 + 0.035)^{25}$$
$$A = 40,000(1.035)^{25}$$
$$A = 40,000(2.36324...)$$
$$A \approx 94,529.81$$

Answer: $\$94,529.81$

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5.) You borrowed $\$1,690$ for $5 \frac{1}{2}$ years at $5.7\%$ compounded semi-annually. What total will you pay back?

* $P = 1,690$
* $r = 0.057$
* $n = 2$ (semi-annually)
* $t = 5.5$ ($5 \frac{1}{2}$ as a decimal)
* Total periods ($n \times t$) = $2 \times 5.5 = 11$.

Calculation:
$$A = 1,690(1 + \frac{0.057}{2})^{11}$$
$$A = 1,690(1 + 0.0285)^{11}$$
$$A = 1,690(1.0285)^{11}$$
$$A = 1,690(1.3545...)$$
$$A \approx 2,289.15$$

Answer: $\$2,289.15$

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6.) Your $\$440$ gets $5.8\%$ compounded annually for 8 years. What will your $\$440$ be worth in 8 years?

* $P = 440$
* $r = 0.058$
* $n = 1$ (annually)
* $t = 8$

Calculation:
$$A = 440(1 + 0.058)^8$$
$$A = 440(1.058)^8$$
$$A = 440(1.5703...)$$
$$A \approx 690.95$$

Answer: $\$690.95$

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7.) Your $\$54,200$ 2 year car loan is at $15.1\%$ compounded annually. What will you have paid for your car after 2 years?

* $P = 54,200$
* $r = 0.151$
* $n = 1$ (annually)
* $t = 2$

Calculation:
$$A = 54,200(1 + 0.151)^2$$
$$A = 54,200(1.151)^2$$
$$A = 54,200(1.3248...)$$
$$A \approx 71,804.16$$

Answer: $\$71,804.16$

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8.) You invest $\$55$ at $10\%$ compounded annually for 3 years. How much will your investment be worth in 3 years?

* $P = 55$
* $r = 0.10$
* $n = 1$ (annually)
* $t = 3$

Calculation:
$$A = 55(1 + 0.10)^3$$
$$A = 55(1.1)^3$$
$$A = 55(1.331)$$
$$A = 73.205$$

(Rounding to nearest cent)

Answer: $\$73.21$

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9.) Your 8 year loan of $\$12,200$ is at $5.3\%$ compounded annually. How much will you have paid in total for your loan?

* $P = 12,200$
* $r = 0.053$
* $n = 1$ (annually)
* $t = 8$

Calculation:
$$A = 12,200(1 + 0.053)^8$$
$$A = 12,200(1.053)^8$$
$$A = 12,200(1.5116...)$$
$$A \approx 18,442.16$$

Answer: $\$18,442.16$

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10.) You invest $\$1,900$ at $4\%$ and it's compounded semi-annually for 3 years. How much will your $\$1,900$ be worth in 3 years?

* $P = 1,900$
* $r = 0.04$
* $n = 2$ (semi-annually)
* $t = 3$
* Total periods ($n \times t$) = $2 \times 3 = 6$.

Calculation:
$$A = 1,900(1 + \frac{0.04}{2})^6$$
$$A = 1,900(1 + 0.02)^6$$
$$A = 1,900(1.02)^6$$
$$A = 1,900(1.12616...)$$
$$A \approx 2,139.71$$

Answer: $\$2,139.71$