I got this question right, but I didn't fully understand one of the concepts that I thought I could use to solve it, but didn't work. Question and my thought process is below:
Question :
If money is invested at r percent interested, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 dollars in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
A. 20,000
B. 15,000
C. 12,000
D. 10,000
E. 9,000
My first method... I understand that because it doubles in 70/8 (8.75) years, which is approximately 9 years, we multiply the initial investment of 5,000 by 4 to get the total amount after 18 (9*2) years.
But then I also remembered that the standard interest formula is:
Interest = (Initial Principal)*(interest)*(time).
So I used a second method because this was a practice question. I used the formula above , and got 7,200, then added it to the 5,000 investment to get 12,200 which is clearly the wrong answer because 20,000 was the correct answer I got by the first method.
I understand whatever works to get the question right, but I wanted to brush this with everybody so someone can explain to me what concept am I getting wrong here? Does the formula not apply to this question, and why?
Thank a bunch!
Question :
If money is invested at r percent interested, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 dollars in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
A. 20,000
B. 15,000
C. 12,000
D. 10,000
E. 9,000
My first method... I understand that because it doubles in 70/8 (8.75) years, which is approximately 9 years, we multiply the initial investment of 5,000 by 4 to get the total amount after 18 (9*2) years.
But then I also remembered that the standard interest formula is:
Interest = (Initial Principal)*(interest)*(time).
So I used a second method because this was a practice question. I used the formula above , and got 7,200, then added it to the 5,000 investment to get 12,200 which is clearly the wrong answer because 20,000 was the correct answer I got by the first method.
I understand whatever works to get the question right, but I wanted to brush this with everybody so someone can explain to me what concept am I getting wrong here? Does the formula not apply to this question, and why?
Thank a bunch!
Whoever runs this store will know it.
