Question

Which of the following statements is corrects?

a) If a loan has a nominal annual rate of 8%, then the effective rate will be less than 8%
b) An in vestment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%
c) the present value id greater than the future value
d) the proportion of the payment that goes toward interest on a fully amortized loan increases over time
e) the present value of a 3 year,$150 ordinary annuity will be lower than the present value of a 3 year,$150 annuity due.

Answer 1

The correct statement is that an investment with a nominal rate of 6% and semiannual payments will have an effective rate that is smaller than 6%.

Step-by-step explanation:

The correct statement out of the given options is: b) An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.

To calculate the effective rate, we need to consider the compounding frequency. In this case, since there are semiannual payments, the interest is compounded twice a year. The effective rate will be lower than the nominal rate due to the effect of compounding.

For example, if the nominal rate is 6%, the effective rate with semiannual compounding might be around 5.99%.

When it comes to amortized loans, the proportion of the payment that goes toward interest actually decreases over time, while the portion that goes toward the principal increases, ultimately leading to the loan's balance being paid off. Lastly, the present value of an annuity due is higher than an ordinary annuity because payments are received at the beginning of each period, therefore, they are discounted for one less period compared to the ordinary annuity's payments received at the end of each period.