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DanielleElmas [232]
3 years ago
7

You started saving for a car when you were in middle school. You have done some research and discovered that it will cost you ab

out $8,000 for a used car that would fit your needs. You were encouraged to invest some of your savings to help you get to your financial goal faster. So far you have saved $6,500. If you invest this money in a savings account with a 1.4% interest rate compounded annually, how long will it take to earn enough money to go purchase the car? Use the compound interest formula A = P (1 + i)n, where A is the accumulated amount, P is the principal, i is the interest rate per year, and n is the number of years. Round your final answer to the nearest tenth
Mathematics
1 answer:
Likurg_2 [28]3 years ago
6 0

Answer: $2,833.47

Step-by-step explanation:

Part 1:

n = [lnA - lnP] / ln(1 + i)

n = [ln15000 - ln10000] / ln(1 + 0.03)

n = [9.6158 - 9.2103] / 0.0296

n = 13.70

13 years, 8 months, and 12 Days

Part 2:

P = A / [(1 + i)n]

P = 15000 / [(1.03)4]

P = 15000 / 1.1255

P = $13,327.31

Part 3:

A = 10000 (1 + 0.04)5

A = $12,166.53

The amount of money you need to save to buy a car at $15,000 would be;

$15,000 - $12,166.53

=> $2,833.47

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<h3>#1</h3>
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Here's one way to convert the number to the ratio of integers.

  1. Count the number of repeating digits. Call this number <em>n</em>. Here, only 5 has an overline, so there is only one repeating digit. That is, <em>n </em>= 1.
  2. Multiply the number by 10^(-n) and subtract that from the original number. Call the result <em>p</em>. Here, doing this gives p=3.25\overline{5}-0.32\overline{5}=3.23
  3. Compute the value <em>q</em> = 1 - 10^(-n). The result of step 2 is <em>q</em> times the original number. Here, <em>q</em> = 1 - 10^-1 = 0.9.
  4. Create the fraction <em>p/q</em>. Note that both <em>p</em> and <em>q</em> have a finite number of decimal digits, so this is easily converted to the ratio of integers, by moving the decimal point an equal number of places in the numerator and denominator. Reduce the resulting fraction as may be required. This is the fraction you're looking for. Here, p/q = 3.23/0.9 = 323/90. No reduction of this fraction is possible.

The fraction you're looking for is ...

3.2\overline{5}=\dfrac{323}{90}

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