Question

11. A two-year certificate of deposit pays an annual effective rate of 9%. The purchaser is offered two options for prepayment penalties in the event of early withdrawal: A - a reduction in the rate of interest to 7%. B loss of three months interest In order to assist the purchaser in deciding which option to select, compute the ratio of the proceeds under Option A to those under Option B if the certificate of deposit is surrendered: a. At the end of 6 months. b. At the end of 18 months.

Answer 1

Assuming interest is compounded annually,

a) Proceeds from option A = (1.07)^(0.42) = 1.03

Proceeds from option B = (1.09)^(0.17) = 1.001

The ratio = 1.03/1.001 = 1.029

So, option A is preferable in this case.

b) Proceeds from option A = (1.07)^(1.42) = 1.1008

Proceeds from option B = (1.09)^(1.17) = 1.1061

The ratio = 1.1008/1.1061 = 0.9952

So, option B is preferable in this case.

PFA the image to understand the formula and subsequent calculation in detail.

Fobmula fh totol bhetubns Ch CD nt A = Px 1 A = Total phoceeds accumulated ofte yech 11 Phincipal amound Annual hate of idesert humbes 11 eahs the amoud ic depaciad fatm humber ef times Hhe indehest ic (onfounded peh yas

DATE: (ay Assuming tnelert is lompoundal amualy Phoceeds xl (2 -hor) Foam aphon 0.42 1:03 2/2 I+ 0.09 Photeeds X O.17 1.001 The 9ratio 1-03 1.024 is 1.001 phuofe akle dhat is Campaunded So, Ophion A is XJ Phoceeds From ophenn A Ix 1.42 1.0) 11 008 X fhom optin Phoceeds BIX/L+0.09 t17 1. 1061 8oal 1-1061 0.99 52 The tatio is 13 pafadle So, Option B is