Which savings account will earn the most interest?
A. at 4 percent simple interest for four years
B. at 4 percent interest compounded for four years
C. at 2 percent interest compounded for four years
D. at 2 percent simple interest for four years

Ask by Hills Lynch. in the United States

Mar 26,2025

Question

Which savings account will earn the most interest?
A. at 4 percent simple interest for four years
B. at 4 percent interest compounded for four years
C. at 2 percent interest compounded for four years
D. at 2 percent simple interest for four years

Ask by Hills Lynch. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

To determine which savings account will earn the most interest, we will calculate the interest earned for each option step by step.

### A. Simple Interest
For simple interest, the formula is:
$$
I = P \times r \times t
$$
where:
- $$ I $$ = interest
- $$ P $$ = principal amount
- $$ r $$ = interest rate (as a decimal)
- $$ t $$ = time (in years)

For option A:
- $$ P = 5000 $$
- $$ r = 0.04 $$
- $$ t = 4 $$

Calculating the interest:
$$
I_A = 5000 \times 0.04 \times 4
$$

### B. Compounded Interest
For compounded interest, the formula is:
$$
A = P \left(1 + \frac{r}{n}\right)^{nt}
$$
where:
- $$ A $$ = the amount of money accumulated after n years, including interest.
- $$ P $$ = principal amount
- $$ r $$ = annual interest rate (decimal)
- $$ n $$ = number of times that interest is compounded per year
- $$ t $$ = number of years

Assuming interest is compounded annually ($$ n = 1 $$), for option B:
- $$ P = 5000 $$
- $$ r = 0.04 $$
- $$ t = 4 $$

Calculating the amount:
$$
A_B = 5000 \left(1 + 0.04\right)^{4}
$$

### C. Compounded Interest
For option C:
- $$ P = 10000 $$
- $$ r = 0.02 $$
- $$ t = 4 $$

Calculating the amount:
$$
A_C = 10000 \left(1 + 0.02\right)^{4}
$$

### D. Simple Interest
For option D:
- $$ P = 10000 $$
- $$ r = 0.02 $$
- $$ t = 4 $$

Calculating the interest:
$$
I_D = 10000 \times 0.02 \times 4
$$

Now, let's calculate the values for each option.
Calculate the value by following steps:
- step0: Calculate:
  $$10000\times 0.02\times 4$$
- step1: Multiply the terms:
  $$200\times 4$$
- step2: Multiply the numbers:
  $$800$$
Calculate or simplify the expression $$ 5000 * (1 + 0.04)^4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5000\left(1+0.04\right)^{4}$$
- step1: Add the numbers:
  $$5000\times 1.04^{4}$$
- step2: Convert the expressions:
  $$5000\left(\frac{26}{25}\right)^{4}$$
- step3: Simplify:
  $$5000\times \frac{26^{4}}{25^{4}}$$
- step4: Rewrite the expression:
  $$625\times 8\times \frac{26^{4}}{25^{4}}$$
- step5: Rewrite the expression:
  $$25^{2}\times 8\times \frac{26^{4}}{25^{4}}$$
- step6: Reduce the numbers:
  $$8\times \frac{26^{4}}{25^{2}}$$
- step7: Multiply:
  $$\frac{8\times 26^{4}}{25^{2}}$$
- step8: Simplify:
  $$\frac{8\times 26^{4}}{625}$$
Calculate or simplify the expression $$ 10000 * (1 + 0.02)^4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$10000\left(1+0.02\right)^{4}$$
- step1: Add the numbers:
  $$10000\times 1.02^{4}$$
- step2: Convert the expressions:
  $$10000\left(\frac{51}{50}\right)^{4}$$
- step3: Simplify:
  $$10000\times \frac{51^{4}}{50^{4}}$$
- step4: Rewrite the expression:
  $$2500\times 4\times \frac{51^{4}}{50^{4}}$$
- step5: Rewrite the expression:
  $$50^{2}\times 4\times \frac{51^{4}}{50^{4}}$$
- step6: Reduce the numbers:
  $$4\times \frac{51^{4}}{50^{2}}$$
- step7: Rewrite the expression:
  $$4\times \frac{51^{4}}{2^{2}\times 25^{2}}$$
- step8: Rewrite the expression:
  $$2^{2}\times \frac{51^{4}}{2^{2}\times 25^{2}}$$
- step9: Reduce the numbers:
  $$1\times \frac{51^{4}}{25^{2}}$$
- step10: Multiply:
  $$\frac{51^{4}}{25^{2}}$$
- step11: Simplify:
  $$\frac{51^{4}}{625}$$
Calculate or simplify the expression $$ 5000 * 0.04 * 4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5000\times 0.04\times 4$$
- step1: Multiply the terms:
  $$200\times 4$$
- step2: Multiply the numbers:
  $$800$$
Now, let's summarize the calculations for each option:

### A. Simple Interest
$$
I_A = 5000 \times 0.04 \times 4 = 800
$$

### B. Compounded Interest
$$
A_B = 5000 \left(1 + 0.04\right)^{4} \approx 5849.29
$$

### C. Compounded Interest
$$
A_C = 10000 \left(1 + 0.02\right)^{4} \approx 10824.32
$$

### D. Simple Interest
$$
I_D = 10000 \times 0.02 \times 4 = 800
$$

### Summary of Interest Earned
- **Option A:** $800
- **Option B:** $5849.29
- **Option C:** $10824.32
- **Option D:** $800

### Conclusion
The account that earns the most interest is **Option C**, which is $$ \$ 10,000 $$ at 2 percent interest compounded for four years, yielding approximately $$ \$ 10,824.32 $$.
Option C earns the most interest.

Which savings account will earn the most interest?
A. at 4 percent simple interest for four years
B. at 4 percent interest compounded for four years
C. at 2 percent interest compounded for four years
D. at 2 percent simple interest for four years

Upstudy AI Solution

Answer

Solution

A. Simple Interest

B. Compounded Interest

C. Compounded Interest

D. Simple Interest

A. Simple Interest

B. Compounded Interest

C. Compounded Interest

D. Simple Interest

Summary of Interest Earned

Conclusion

The Deep Dive

Related Questions

Latest Arithmetic Questions

Which savings account will earn the most interest? A. at 4 percent simple interest for four years B. at 4 percent interest compounded for four years C. at 2 percent interest compounded for four years D. at 2 percent simple interest for four years

Upstudy AI Solution

Answer

Solution

A. Simple Interest

B. Compounded Interest

C. Compounded Interest

D. Simple Interest

A. Simple Interest

B. Compounded Interest

C. Compounded Interest

D. Simple Interest

Summary of Interest Earned

Conclusion

The Deep Dive

Related Questions

Latest Arithmetic Questions

Which savings account will earn the most interest?
A. at 4 percent simple interest for four years
B. at 4 percent interest compounded for four years
C. at 2 percent interest compounded for four years
D. at 2 percent simple interest for four years