On the day that Jennifer was born, her rich uncle set up a trust for her and invested $20000 at a 8% annual interest rate compounded monthly. After how many months will the investment first be worth at least $77000? (integer answer)

Question

ahsome · Answer

The equation you use for compound interest is:
$$FV = PV × (1+r)^n$$
Where:
$$FV=Future Value$$
$$PV=Present Value$$
$$R=Rate$$
$$n=time$$
To find the time, use this equation
$$n = ln(FV / PV) / ln(1 + r)$$
Where ln=Natural logarithm. Most calculators have this button.
Substitute the values
$$n = ln(77000 / 20000) / ln(1 + 1.08)$$
This will give you the answer, @imyint

ahsome · Answer

For more info: http://www.mathsisfun.com/money/compound-interest.html

aum · Answer

Since the interest is compounded MONTHLY (not annually), the interest rate in decimal should be divided by 12.

ahsome · Answer

^^ Yes ^^. Although this is not always the case if the rate itself is monthly

aum · Answer

Denominator: ln( 1 + 0.08/12)    (not 1.08/12).

ahsome · Answer

Really? I thought it would be 1.08 as then you would get the percentage, but you probably know way more than me ;)

Rewritten equation:
$$n=\frac{ln(77000/20000)}{ln(1+(0.08/12))}$$

aum · Answer

Round your answer to the next highest integer because the question asks: "AT LEAST $77000? (INTEGER answer)"