# Algebra

How long, to the nearest tenth of a year, will it take \$12,500 to grow to \$20,000 at 6.5% annual interest compounded quartely? (Use the formula for compound interest with n compoundings per year to solve for t.)

1. 👍 0
2. 👎 0
3. 👁 194
1. With k compounding a year, the compound interest formula becomes:

FV = PV*Rkn
where
FV=future value
PV=present value
r=annual rate of interest, in fraction.
For example, 0.12 stands for 12%.
k=number of compounding a year, 4 for compounding every three months.
n=number of years
R=compounding rate, = 1+r/k

For example,
at 8% annual interest compounded 4 times a year, \$10000 will accumulate to \$20000 in n years.
20000=10000*(1+0.08/4)4n
divide by 10000,
1.024n = 2.0
take log on both sides
4n log(1.02) = log(2.0)
n = (1/4)log(2)/log(1.02)
=8.75 years

1. 👍 0
2. 👎 0
posted by MathMate
2. Still not sure what the answer is.

1. 👍 0
2. 👎 0
posted by Roger

## Similar Questions

1. ### Algebra

Invest \$2800 @ 4.7% a year (compound). How long it will take to double the amount invested to the nearest tenth of the year?

asked by Geo on December 9, 2017
2. ### College math

A rock is thrown from the top of a tower that is 400 feet tall. If its height above the ground can be modeled by h = -16t2 + 64t +400 where h is in feet, and t is in seconds. To the nearest tenth of a second, how long does it take

asked by Michala on July 20, 2014
3. ### college

how long will it take \$1250 to become \$2000 at 3.5% interest compounded continuously? (round to nearest tenth of a year)

asked by Anonymous on September 30, 2010
4. ### Math

A park district paid their director \$19,500 in 1960. In 2000 that same park district paid their director \$40,000. Determine the average rate of increase per year to the nearest tenth of a percent This is my answer

asked by Natatlie on March 19, 2010
5. ### Math, are they all right?

1. A student raises her grade average from a 75 to a 90. What was the percent of increase in the student’s grade average? Round your answer to the nearest tenth of a percent, if necessary. A: 20% B: 16.7% C: 8.3% D: 15% *** 2.

asked by Lizzie on February 2, 2016
6. ### clackamas

Consider a \$100 investment earning 12% compounded quarterly. How long will it take to triple your money? Round your answer to the nearest tenth of a year.

asked by Anonymous on February 11, 2013
7. ### Math

Find out how long it takes a ​\$3,100 investment to double if it is invested at 7% compounded monthly. Round to the nearest tenth of a year.

asked by Ciara on October 29, 2017

find out how long it takes a \$2700 investment to double if it is invested by 7% compounded semiannually. Round to the nearest tenth of a year . Use the formula A=P[1+r/n]^nt

asked by tasha on February 19, 2009
9. ### How long will it take the investment to double?

\$3,600 is invested in an account at an annual interest rate of 4.8% compounded continuously. How long, to the nearest tenth of a year, will it take the investment to double in size?? Any help would be appreciated.

asked by Naomi on October 10, 2014
10. ### geometry

round to the nearest tenth. a rectangular plot of land is 80 meters wide and 98 meters long. Find the length of the diagonal and if necessary, round to the nearest tenth.

asked by Ariana on September 1, 2013

More Similar Questions