# Algebra II

posted by Annie

I'm pretty confused about these problems. We're learning growth and decay, but there are quite a few formulas.

1. Suppose \$500 is invested at 6% annual interest compounded twice a year. When will the investment be worth \$1000?

2. Suppose \$500 is invested at 6% annual interest compounded continuously. When will the investment be worth \$1000?

... I'm really confused

1. Damon

If the annual interest is 6 percent every half year the amount in the account is multiplied by 1.03 every half year.
so after n half years the account will be worth:
\$500 * (1.03)* (1.03) * (1.03) etc n times
or
\$500 * (1.03)^n
so do the problem in half years
\$500 * (1.03)^n = 1000
1.03^n = 2
take the log of both sides remembering that log x^y = y log x
n * .012837 = .301030
n = 23.45 half years = 11.7 years
-----------------------------------
Now for the continuous problem you either have to know the formula from your text book or know calculus.
Since I do not have a textbook, I will figure it out and find the formula
dy/dt = .06 y
dy/y = .06 dt
ln y = .06 t + c
y = e^(.06 t + c) = C e^.06 t
when t = 0, y = \$500 so
THIS NEXT LINE IS PROBABLY IN YOUR TEXT
y = 500 e^.06 t
so we want
1000 = 500 e^.06 t
ln 2 = .06 t
.693147 = .06 t
so t = 11.55 years
Just a little better than compounding twice a year

2. Damon

By the way, a rule of thumb is that your money doubles in ten years at 7% interest.

## Similar Questions

1. ### math/algebra

Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1+r/2)^2represents the value of the investment after 1 year. Rewrite this expression …
2. ### College Algebra

Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1+r/2)^2 represents the value of the investment after 1 year. Rewrite this expression …
3. ### Finance

. (TCO 3) Mark deposited \$1,000 today, in an account that pays eight percent interest, compounded semi-annually. Which one of the following statements is correct concerning this investment?
4. ### math

Suppose that you have \$12,500 to invest over a 4 year period. There are two accounts to choose from: 4.5% compounded monthly or 4.3% compounded continuously. a. Write the formula for the first accountâ€™s compound interest for n compounding …
5. ### algebra

Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial represents the value of the investment after 1 year. Rewrite this expression without …
6. ### algebra

An investment adviser invested \$14,000 in two accounts. One investment earned 4% annual simple interest, and the other investment earned 2.5% annual simple interest. The amount of interest earned for 1 year was \$458. How much was invested …
7. ### Still confused

An investment adviser invested \$14,000 in two accounts. One investment earned 4% annual simple interest, and the other investment earned 2.5% annual simple interest. The amount of interest earned for 1 year was \$458. How much was invested …
8. ### college algebra

An investment initially worth \$5300 earns 7.7% annual interest, and an investment initially worth \$8000 earns 5.6% annual interest, both compounded annually. How long will it take for the smaller investment to catch up with the larger …
9. ### Algebra 1

1.the number of bacteria present in a colony is 180 at 12 noon and the bacteria grows at a rate of 22% per hour. how many will be present at 8pm?
10. ### college algebra

I'm completely drawing a blank on how to do this. A woman has \$500,000 invested into two real estate properties. One yields an annual return on 12% and the other returns 15% per year on her investment. Her total annual return from …

More Similar Questions
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://www.jiskha.com/display.cgi?id=1212954531", "fetch_time": 1532000549000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2018-30/segments/1531676590866.65/warc/CC-MAIN-20180719105750-20180719125750-00212.warc.gz", "warc_record_offset": 914392611, "warc_record_length": 4544, "token_count": 1012, "char_count": 3921, "score": 4.15625, "int_score": 4, "crawl": "CC-MAIN-2018-30", "snapshot_type": "latest", "language": "en", "language_score": 0.9271876215934753, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00026-of-00064.parquet"}