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lora16 [44]
3 years ago
7

$2000 was borrowed for 4 years with an interest rate of 3% compounded annually. What is the total amount owed at the end of the

4 years.

Mathematics
2 answers:
coldgirl [10]3 years ago
5 0

$2,251.02

<h3>Further explanation</h3>

<u>Given:</u>

  • Amount of initial money borrowed = $2,000
  • Time of borrowing = 4 years
  • Interest rate = 3% compounded annually, therefore 3% equal to 0.03

<u>Question:</u>

What is the total amount owed at the end of the 4 years?

<u>The Process:</u>

Compound interest is the interest earned from the initial amount and the interest earned previously. The formula for the balance A of the loan with compound interest is

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

  • P = principal (initial amount)
  • r = annual interest rate (in decimal form)
  • t = time (in years)
  • n = the number of periods of interest is compounded per year

For interest compounded yearly, we can substitute 1 for n in the formula.

Let us calculate how much the total amount owed at the end of the 4 years.

\boxed{ \ A = 2,000(1 + 0.03)^{4} \ }

\boxed{ \ A = 2,000(1.03)^{4} \ }

\boxed{ \ A = 2,000 \times 1.12550881 \ }

\boxed{ \ A = 2,251.01762 \ } \rightarrow \boxed{ \ M \approx 2,251.02 \ }

Thus, the total amount owed at the end of the four years is $2,251.02.

- - - - - - -

Notes

What if the interest rate of 3% is compounded monthly (n = 12)?

\boxed{ \ A = 2,000(1 + \frac{0.03}{12})^{12 \times 4} \ }

\boxed{ \ A = 2,000(1.0025)^{48} \ }

\boxed{ \ A = 2,000 \times 1.127328021 \ }

\boxed{ \ A = 2,254.656042 \ } \rightarrow \boxed{ \ M \approx 2,254.66 \ }

\boxed{\boxed{ \ M = \$ 2,254.66 \ }}

<h3>Learn more</h3>
  1. Melanie is looking for a loan brainly.com/question/2708838
  2. How much money did Jenny earn in all?  brainly.com/question/2068148#
  3. What was the sale price of the house? brainly.com/question/1049004

Keywords: $2000, borrowed, for 4 years, with, an interest rate, 3%, 0.03, compounded annually, what is the total amount owed at the end of the 4 years

kompoz [17]3 years ago
4 0

Answer:

\$2,251.02  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the total amount owed  

P is the amount of money borrowed

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=4\ years\\ P=\$2,000\\ r=3\%=3/100=0.03\\n=1  

substitute in the formula above  

A=2,000*(1+\frac{0.03}{1})^{1*4}  

A=2,000*(1.03)^{4}  

A=\$2,251.02  

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