Question

$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.

Answer 1

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  

$A=2,000*(1+\frac{0.03}{1})^{1*4}$  

$A=2,000*(1.03)^{4}$  

$A=\ 2,251.02$  

Answer 2

$2,251.02

Further explanation

Given:

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

Question:

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

The Process:

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)?

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

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

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

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

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

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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