Felipe received a $$ \$ 1200 $$ bonus. He decided to invest it in a 3 -year certificate of deposit (CD) with an annual interest rate of $$ 1.27 \% $$ compounded quarterly. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Assuming no withdrawals are made, how much money is in Felipe's account after 3 years? (b) How much interest is earned on Felipe's investment after 3 years? $$ \$ \square $$

Question

UpStudy AI · Accepted Answer

To find the amount of money in Felipe's account after 3 years, we can use the formula for compound interest:

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

where:
- $$ A $$ is the amount of money in the account after $$ t $$ years,
- $$ P $$ is the principal amount (initial investment),
- $$ r $$ is the annual interest rate,
- $$ n $$ is the number of times the interest is compounded per year,
- $$ t $$ is the time in years.

Given:
- $$ P = \$1200 $$ (initial investment),
- $$ r = 1.27\% = 0.0127 $$ (annual interest rate),
- $$ n = 4 $$ (compounded quarterly),
- $$ t = 3 $$ years.

Substitute the values into the formula:

$$ A = 1200 \left( 1 + \frac{0.0127}{4} \right)^{4 \cdot 3} $$

Now, we can calculate the amount of money in Felipe's account after 3 years.
Calculate the value by following steps:
- step0: Calculate:
  $$1200\left(1+\frac{0.0127}{4}\right)^{4\times 3}$$
- step1: Divide the terms:
  $$1200\left(1+\frac{127}{40000}\right)^{4\times 3}$$
- step2: Add the numbers:
  $$1200\left(\frac{40127}{40000}\right)^{4\times 3}$$
- step3: Multiply the numbers:
  $$1200\left(\frac{40127}{40000}\right)^{12}$$
- step4: Simplify:
  $$1200\times \frac{40127^{12}}{40000^{12}}$$
- step5: Rewrite the expression:
  $$400\times 3\times \frac{40127^{12}}{40000^{12}}$$
- step6: Rewrite the expression:
  $$400\times 3\times \frac{40127^{12}}{8000^{12}\times 5^{12}}$$
- step7: Rewrite the expression:
  $$20^{2}\times 3\times \frac{40127^{12}}{20^{36}\times 5^{12}}$$
- step8: Reduce the numbers:
  $$3\times \frac{40127^{12}}{20^{34}\times 5^{12}}$$
- step9: Multiply the fractions:
  $$\frac{3\times 40127^{12}}{20^{34}\times 5^{12}}$$
The amount of money in Felipe's account after 3 years is approximately $1246.53.

To find the interest earned on Felipe's investment after 3 years, we can subtract the initial investment from the final amount:

Interest = Final Amount - Initial Investment

Interest = $1246.53 - $1200

Interest = $46.53

Therefore, the interest earned on Felipe's investment after 3 years is $46.53.
After 3 years, Felipe has $1,246.53 in his account. He earned $46.53 in interest.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Economics Questions