Question 6 0.5 pts The city of Lincolnshire has a deal with the local youth cent

Question

Question 6 0.5 pts The city of Lincolnshire has a deal with the local youth center to help pay for maintenance. The city will pay $4243 each month and increase its payment by 1.5% each subsequent month. The city has committed to paying this maintenance for 12 years. How much should the city set aside today to pay for this future maintenance if the bank pays a nominal annual interest rate of 18%, compounded monthly? WI Enter your answer as follows: 12345 Round your answer. Do not use a dollar sign ("$"), any commas("") or a decimal point(

Explanation / Answer

Initial amount = $4243

payment increase per month = 1.5%

Duration for which the amount is to be paid = n = 12 years = 144 months

Step 1. We have to find the total amount to be paid by the end of 12 years for the maintenance considering the interest of 1.5% each subsequent month

= 4243 *12*12 + Interest for 144 months over principle amount of 4243 $ = 4243 {1+ (1.5/100)} 144

= 610992 + 36206.21 = 647198.214 $

Step 2 : Let the amount to be kept aside = X $

bank pays nominal annual interest of 18% compunded per month

therefore 36206 = X {1+ 18/100}12 = 7.287X

X = 36206/7.287 = 4968.57

Therefore the amount to be kept aside = $4968.54

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