Question

1. At what annual interest rate capitalizable each semester equals six semi-annual advance deposits of $ 16670 at a present value of $ 70000. What is the effective rate?

2.To pay for an article with a cash value of $ 132800, we were asked for 25 bi-monthly payments of $ 8,148 each. If the first payment is immediately, obtain the capitalizable annual interest rate every two months and the effective rate.

Answer 1

(1) Compounding Frequency = Quarterly (capitalized per semester), Payment Frequency = 6 months (semi-annual)

Advance Semi-Annual Payments = $ 16670 and Present Value = $ 70000, Number of Semi-Annual Payments = 6

Let the semi-annual discount rate be R

Therefore, 70000 = 16670 x (1/R) x [1-{1/(1+R)^(6)}] x (1+R)

Using EXCEL's Goal Seek Function/ a financial calculator/ hit and trial method to solve the above equatio, we get:

R = 0.17002529 or 17.002529 % ~ 17 %

Quarterly Yield = (1.17)^(1/2) - 1 = 0.08166 or 8.166%

Effective Annual Yield = [1+0.08166]^(4) - 1 = 0.3689 or 36.89 %

NOTE: Please raise a separate query for the solution to the second unrelated question, as one query is restricted to the solution of one complete question with up to four sub-parts.