# What is the annual nominal interest rate of a $\$500$loan payable in two weeks at$\$675$? What is the effective annual interest rate?

What is the annual nominal interest rate of a $\$500$loan payable in two weeks at$\$675$? What is the effective annual interest rate? Assume it compounds $26$ times in a year, how much money would be owed at the end of the year?

I think if I could determine the nominal interest rate the rest of the problem would flow well from there. I'm aware that it's a 35% interest rate compounded every two weeks but I'm unaware of how translate this to an annual nominal rate.

• Welcome to MathSE. When you pose a question here, it is expected that you share your own thoughts on the problem. For an exercise such as this, you should indicate what you have tried and where you are stuck so that you receive responses appropriate to your skill level. – N. F. Taussig Apr 16 '17 at 22:57
• Okay, well, I think if I could determine the annual nominal interest rate the rest of the problem would flow well from there. I'm aware that it's a 35% interest rate compounded every two weeks but I'm unaware of how to translate this to an annual nominal rate. – The who slips Apr 16 '17 at 23:05

Since $675/500 = 1.35$ you've correctly calculated the $35\%$ rate for two weeks. After two more weeks you'd owe $$1.35\times 1.35 \times \500 = 1.35^2 \times \500 = 1.8225 \times \500 = \911.25$$ for a four week interest rate of $82.25\%$.
• I think the nominal annual rate is just $26 \times 35\% = 910\%$. My calculation says you owe more than $\$1.2\$ million so the effective rate is much much more. That's what the compounding does. – Ethan Bolker Apr 16 '17 at 23:54