Monday

December 22, 2014

December 22, 2014

Posted by **Roger** on Friday, December 3, 2010 at 10:48am.

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.)

- Algebra -
**MathMate**, Friday, December 3, 2010 at 8:02pmWith k compounding a year, the compound interest formula becomes:

FV = PV*R^{kn}

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,

1.02^{4n}= 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

- Algebra -
**Roger**, Sunday, December 5, 2010 at 7:11pmStill not sure what the answer is.

**Answer this Question**

**Related Questions**

algebra - How long, to the nearest day, will it take $25,000 to grow to $500000...

Algebra - How long will it take $7,000 invested at 5.5% compounded daily to grow...

algebra - The amount of money in an account with continuously compounded ...

algebra 2 - The amount of money in an account with continuously compounded ...

College Algebra - 20. Growth of an Account If Russ (see Exercise 19) chooses the...

How long will it take the investment to double? - $3,600 is invested in an ...

college algebra - how long would it take $3,100 to grow to $8,800 if the annual ...

math - So I think I have got these down I just really want to double check the ...

Math - If $ 2500 is invested in an account that pays interest compounded ...

Pre-Cal - This exercise is based on the following table, which lists interest ...