Claire has borrowed $\$5,\!000$. She plans to pay off the loan in full after two payments. She will make one payment in 3 years, then another payment in 6 years. The second payment will be exactly double the amount of the first payment. How much is the first payment if the interest rate of the loan is $8.5\%$, compounded annually? Express your answer as a dollar value rounded to the nearest cent.

Question

Reiny · Accepted Answer

Don't try fancy codes here, they don't work.
I will read that as $5,000

Pick your "time spot" at 6 years, then
2x + x(1.085)^3 = 5000(1.085)^6
x(2 + 1.08r^2) = 8157.34
x = 8157.34/3.277289... = $2489.05

AoPS Administrator · Answer

Cheater. This is an Alcumus QUESTION !!!!!

AoPS Administrator · Answer

We have tracked your I.P. and will take immediate action for violating the honor code.

person · Answer

lmfao no ur not and aops administrator stop the cap

AoPS Administrator · Answer

You have been IP banned from AoPS.

can confirm · Answer

Let Claire's first payment be $x$, so her second one is $2x$. The present value of the first payment is $(x)/(1.085)^3$ and the present value of the second is $(2x)/(1.085)^6$. The sum of these present values must equal $\$5,\!000$, the amount Claire borrows today:\[\frac{x}{1.085^3} + \frac{2x}{1.085^6} = \$5,\!000 \implies x = \boxed{\$2,\!489.05}.\]

confirmed the first answer

g · Answer

YOU STINKIN CHEATER

AoPS (not actually) · Answer

did someone just pretend to say they're the aops admin this is serious cheating but i dont think they're the real aops admin but who knows

A guy who says stuff · Answer

If it was an aops admin you could use a vpn