Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?

Question $12$ options:

a$)$

A $30-$year, $$150,000$ amortized mortgage will have larger monthly payments than an otherwise similar $20-$year mortgage.

b$)$

Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit.

c$)$

A bank loan's nominal interest rate will always be equal to or less than its effective annual rate.

d$)$

If an investment pays $10\%$ interest, compounded annually, its effective annual rate will be less than $10\%.$

e$)$

The present value of a $5-$year, $$250$ annuity due will be lower than the PV of a similar ordinary annuity.