Question

collegelink//course resource/section/7470/assignment/14040 5 Arpandeep Kaur K n 4 (3) n 5 (2) -n 6(1) en 7 (2) Question 11 of 13 How much more would you need to deposit at the end of every month to accumulate $288,500 over 22 years if the interest rate earned is 5.5% compounded annually instead of 5.5% compounded monthly? on 8 (1) on 9 (2) On 10 (1) on 11 (1) on 12 (1) on 13 (1) Round to the nearest cent Next Question ch 26th 11:40 am Submit

Answer 1

Amount needed after 22 years = $288500

Since money need to be deposited at the end of the month so it is an ordinary annuity.

So annuity using FV formula is

PMT = FV*(r)/((1+r)^(t) - 1)

So when interest rate is 5.5% compounded annually, FV = 288500, t = 22

So, PMT = 288500*(0.055)/((1 + 0.055)^22 - 1) = $7059.95, So annual payment = $7059.95

When interest rate is 5.5% compounded monthly, so effective annual rate = (1+APR/12)^12 - 1

So, EAR = (1 + 0.055/12)^12 - 1 = 5.64%

So, here annual payment PMT = 288500*(0.0564)/((1 + 0.0564)^22 - 1) = $6942.02

So when interest rate is 5.5% compounded annual, an extra of (7059.95-6942.02) = $117.93 need to made every year.