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A savings account in a bank yields 0.25% compound interest annually. If you deposited Php 25,000.00 for 4 years, compute for the following: (a) The future value of the money invested. Answer (b) The interest paid to you by the bank. Answer

Sagot :

UK2019

✏️INTEREST

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[tex]\underline{\mathbb{PROBLEMS:}}[/tex]

- A savings account in a bank yields 0.25% compound interest annually. If you deposited Php 25,000.00 for 4 years, compute for the following:

  • a. The future value of the money invested.
  • b. The interest paid to you by the bank.

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[tex]\underline{\mathbb{ANSWERS:}}[/tex]

[tex]\qquad\LARGE\rm»\:\: a. \: \green{Php. \: 25\text,250}[/tex]

[tex]\qquad\LARGE\rm»\:\: b. \: \green{Php. \: 250}[/tex]

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[tex]\underline{\mathbb{SOLUTIONS:}}[/tex]

- Determine what are the given.

  • [tex]P=25\text,000[/tex]
  • [tex]r = 0.25\% = 0.0025[/tex]
  • [tex]t = 4[/tex]
  • [tex]n = 1[/tex]
  • [tex]FV = \:? [/tex]

a. What is the future value of the money invested?

- We can use the Compound Interest Formula to find the future value of the money invested in the bank.

[tex] \begin{aligned}& \bold{ \color{lightblue}Formula:} \\& \boxed{A = P \bigg(1 + \frac{r}{n} \bigg)^{nt} } \end{aligned}[/tex]

  • [tex] \begin{aligned}{A = 25\text,000 \bigg(1 + \frac{0.0025}{1} \bigg)^{(1)(4)} } \end{aligned}[/tex]

  • [tex] \begin{aligned}{A = 25\text,000 \bigg(1 + \frac{0.0025}{1} \bigg)^{4} } \end{aligned}[/tex]

  • [tex] \begin{aligned}{A = 25\text,000 \big(1 + 0.0025 \big)^{4} } \end{aligned}[/tex]

  • [tex] \begin{aligned}{A = 25\text,000 \big(1.0025 \big)^{4} } \end{aligned}[/tex]

  • [tex] \begin{aligned}{A = 25\text,000 \big(1.01 \big) } \end{aligned}[/tex]

  • [tex] \begin{aligned}{A = 25\text,250} \end{aligned}[/tex]

[tex]\therefore[/tex] Php. 25,250.00 is the future value of the money invested.

[tex]\rm[/tex]

b. What is the interest paid to you by the bank?

- Find the interest paid by the bank by subtracting the Future Value Amount by Principal Amount.

  • [tex]I = FV - P[/tex]

  • [tex]I = 25\text,250 - 25\text,000[/tex]

  • [tex]I = 250[/tex]

[tex]\therefore[/tex] Php. 250 is the interest paid by the bank.

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