“Sarah Invested $38,700”: Should the interest in the 36th month be far greater than the interest of $200 in the first month?

Question

Should the interest in the 36th month be far greater than the interest of $200 in the first month?

Answer

Great question! It will be greater, but it won't be far greater.

Even if we round up to 40,000 and increase by 10% every year for three years, we have:

1.3 * 40,000 = 52,000

This is because we add 10% to our principle of 40,000 every year for 3 years, at the end of the 3 years we will have 30% more principle than we started with, or 1.3 times the principle.

And .5% of 52,000 is about 250—still less than 300, not even close to 714, which is the next largest answer choice.

I took .5% (not 5%) because that is the monthly interest. Remember, it's 6.2% interest compounded monthly, so we have:

6.2 (or about 6) / 12 = .5% interest per month.

Of course, it would be fine to use the calculator here to multiply something like:

40,0001.06 * 1.06 * 1.06.5 / 100 = 238

40,000 is the principle, increasing about 6% per year, so we multiply by 1.06 (100% + 6%) three times. Then, we multiply by .5/100 because our monthly interest rate is .5%.

Link

http://gre.magoosh.com/questions/4206