Question

Your new job offers a savings plan that pays 0.75 percent in interest each month. You can't participate in the plan, however, until you have 8 years with the company. At that time you will start saving $350 a month for the next 20 years How much will you have in this savings account in 28 years? Round your answer to two decimals. $ 233,760.40 Another perk of your new job is that, after 8 years with the company, you will also get an increase of $175 in your monthly salary. Assume you would stay with the company for 20 more years after getting the salary increase, and that you discount at 0.75 percent each month. What is this salary increase worth to you today? Round your answer to two decimals Snir

Answer 1

PartPart 1: Savings planWe are asked to find the amount of money that will be in the savings account in 28 years if the new job offers a savings plan that pays 0.75 percent in interest each month and the employee starts saving $350 a month for the next 20 years after 8 years with the company.The interest rate is given per month. Therefore, the annual interest rate will be as follows:Annual interest rate=0.75%×12=9%Using the formula for future value of an annuity, we get:Future value of annuity= PMT × [(1 + r)n – 1] / rWhere, PMT = Payment per period, r = interest rate per period, n = number of periods.FV= 350 × [(1 + 0.09/12)^(20×12)] / (0.09/12)=350 × [(1.0075)^(240)] / (0.0075)= $233,760.40Therefore, the amount of money that will be in the savings account in 28 years is $233,760.40.Part 2: Salary increaseAfter 8 years of working with the company, the employee gets an increase of $175 in their monthly salary. We are asked to calculate what this increase will be worth to them today if they discount at 0.75 percent each month.The annual discount rate is:Annual discount rate=0.75%×12=9%Discounting the salary increase at 9% per year for 20 years gives:Present value of annuity= PMT × [1 – (1 + r)^-n] / rWhere, PMT = Payment per period, r = discount rate per period, n = number of periods.PV= 175 × [1 – (1 + 0.09/12)^(-20×12)] / (0.09/12)=175 × [1 – (1.0075)^(-240)] / (0.0075)= $17,874.89Therefore, the salary increase is worth $17,874.89 to the employee today.