Question

Which of the following statements is CORRECT?

	a.	The proportion of the payment that goes toward interest on a fully amortized loan increases over time.
	b.	If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.
	c.	The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.
	d.	If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.
	e.	An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.

Answer 1

OPTION (a) : IS WRONG

AS TIME PASSES, THE OUTSTANDING BALANCE OF LOAN DECREASES, SO INTEREST PAYMENT ALSO DECREASES

OPTION (b) : IS WRONG.

EFFECTIVE RATE CAN BE EQUAL TO OR GREATER THAN NOMINAL RATE

EFFECTIVE RATE USES COMPOUNDING SO EXCEPT YEARLY COMPOUNDING, IN ALL OTHER CASES EFFECTIVE RATE IS HIGHER THAN NOMINAL RATE

OPTION (c) : IS CORRECT.

ANNUITY DUE IMPLIES PAYMENT RECEIVED FROM TODAY AND ORDINARY ANNUITY IMPLIES PAYMENT RECEIVED AFTER A YEAR, SO ANNUITY DUE IS DISCOUNTED FOR ONE LESS TIME THAN ORDINARY ANNUITY.

SO ANNUITY DUE HAS HIGHER VALUE THAN ORDINARY ANNUITY

OPTION (d) : IS WRONG

IF COMPOUNDING IS ANNUALLY, THEN I SAID IN OPTION (b) EFFECTIVE RATE, NOMINAL RATE & PERIODIC RATES WILL BE EQUAL.

OPTION (e) : IS WRONG

IF SEMI ANNUAL COMPOUNDING IS GIVEN

EFFECTIVE RATE = (1+ 0.06/2)^2 - 1 = 6.09% WHICH IS HIGHER THAN NOMINAL RATE OF 6% (THUMBS UP PLEASE)