I'm reading through Marcel B. Finan's A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2 on my own and I want to make sure I understand discounting. To check that I understand it correctly, I'm copying two of his questions (from page 63, section 8), and my answers, and asking y'all to correct my work.
The amount of interest earned on A for one year is \$336, while the equivalent amount of discount is \$300. Find A.
- $(A-300)(1+i)=A$ and
so we get $300(1+i)=336$ so that $i=.12$. Then $.12A=336$ so $A=2800$.
Calculate the accumulated value at the end of 3 years of 15,000 payable now assuming an interest rate equivalent to an annual discount rate of 8%.
It's just $15000(100/92)^3$, or $19263.17\ldots$.