Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

You deposit $300 in a savings account that pays 6% interest compounded semiannually. How much will you have at the middle of the first year? How much at the end of one year?

Sagot :

absor201

Answer:

  • The total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 300.00 at a rate of 6% per year  compounded 2 times per year  over 0.5 years is $ 309.00.

  • The total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 300.00 at a rate of 6% per year  compounded 2 times per year  over 1 year is $ 318.27.

Step-by-step explanation:

a)  How much will you have at the middle of the first year?

Using the formula

[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]

where

  • Principle = P
  • Annual rate = r
  • Compound = n
  • Time  = (t in years)
  • A = Total amount

Given:

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 0.5 years

To determine:

Total amount = A = ?

Using the formula

[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]

substituting the values

[tex]A=300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(0.5\right)}[/tex]

[tex]A=300\cdot \frac{2.06}{2}[/tex]

[tex]A=\frac{618}{2}[/tex]

[tex]A=309[/tex] $

Therefore, the total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 300.00 at a rate of 6% per year  compounded 2 times per year  over 0.5 years is $ 309.00.

Part b) How much at the end of one year?

Using the formula

[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]

where

  • Principle = P
  • Annual rate = r
  • Compound = n
  • Time  = (t in years)
  • A = Total amount

Given:

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 1 years

To determine:

Total amount = A = ?

so using the formula

[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]

so substituting the values

[tex]A\:=\:300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(1\right)}[/tex]

[tex]A=300\cdot \frac{2.06^2}{2^2}[/tex]

[tex]A=318.27[/tex] $

Therefore, the total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 300.00 at a rate of 6% per year  compounded 2 times per year  over 1 year is $ 318.27.

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.