Compound Interest II

Compound Interest II

AnalysisPage 1

Compound Interest II

  1. Your child has just started high school and you are already planning for college. Suppose that you plan to need $20,000 in forty-eight months' time for your child’s first year in college. You want to invest in an instrument yielding4.5% interest, compounded monthly. How much should you invest?
  1. You just moved into your new apartment and you stop by Ikea for a few things to make your apartment look livable. You end up spending $1200 and use the Ikea credit card that says you don’t have to make a payment for an entire year. If you plan to pay the bill in full one year from now, how much money would you have to invest at 4% interest compounded continuously?
  1. You plan to redo the garden in your new apartment and go to Home Depot with $300. Unfortunately, the trip costs a little more than you think it will. Mulch, bushes, flowers, and the like cost you $325 and you decide to put the bill on your new Home-Depot credit card. Home Depot’s credit card offers you 6 months no interest with no payment necessary. If you want to pay off your balance in full in 6 months, what interest rate should you find to invest your $300, compounded continuously, so you have enough money to pay the bill when it is due?
  1. It has been said that a millionaire could live off the interest he earns from his investments. Find the yearly interest amount of $1,000,000 compounded continuously at 3.5%.
  1. How many years would it take an investment to double in value at 6% compounded monthly?
  1. A child is born and a savvy investor immediately begins to think about sending his child to college. What lump sum would he have to invest in an account earning 5%, compounded continuously, so that it will grow to $25,000 for his child’s first year college tuition in 18 years?
  1. Your good friend has to have the newest and the best everything and uses a credit card to have it all. The bill jumps to $1200 very quickly and there is no way to pay it back. If no payments are made for three months, what will the new bill be if interest is compounded continuously at 24%?
  1. On your daughter’s first birthday, you take all her gift money totaling $875 and invest it at a rate of 3.8% compounded continuously. How much will her investment be worth on her 18th birthday?
  1. Zach borrows $3740 at 14% interest compounded quarterly. When Zach pays the loan back 6 years later, what is the total amount that Zach ends up repaying ?
  1. Tom plans to invest x dollars into a savings account that pays interest at an annual rate of 8%, compounded quarterly. Approximately what amount is the minimum that Tom will need to invest to earn over $100 in interest within 6 months?
  1. Staying up late one night, you turn on QVC to watch their commemorative coin sale. They offer you a money back guarantee if their $225 shiny, gold plated, presidential quarter collection doesn’t increase in value at 4% compounded continuously. What will this investment be worth in 3 years?
  1. What rate, compounded continuously, should a bank offer if you want your investment to double in value in 9 years?
  1. Timmy and Tommy each invest $600 in the bank. Timmy earns 4% compounded continuously, while Tommy earns 4.25% compounded semiannually. Who will have more money and by how much after 10 years?
  1. Suppose Karen wants $1000 after investing her money for two years. If she finds a 4% CD compounded continuously, how much should she deposit in order to meet her goal?
  1. William wants to have a total of $4000 in two years so that he can put a hot tub on his deck. He finds an account that pays 5% interest compounded continuously. How much should William put into this account so that he’ll have $4000 at the end of two years?
  1. Suppose William, from our last example, only has $3500 to invest but still wants $4000 for a hot tub. He finds a bank offering 5.25% interest compounded continuously. How long will he have to leave his money in the account to have $4000?
  1. Melissa needs $4205 for the car she wants. She has $2079 saved in the bank. The bank agrees to lend her the rest at 15% interest compounded continuously. Assuming all the borrowed amount is paid back in one year plus the interest, how much does she pay the bank in total.
  1. In 1626, Peter Minuit paid 60 guilders, or about $24, to the Indians for ManhattanIsland. What would be the value of that $24 in 2011 if it would have been invested at 5% annual interest compounded annually since then?
  1. Mr. Riley deposits $500 into an account that pays 10% interest, compounded semiannually. How long will it take Mr. Riley to earn $25 in interest?
  1. Paul invested $6,000 in an account for 3 years, compounded continuously. What interest rate would he have to earn to $400 in interest?
  1. If Marie wants to invest $4,500 in an account earning 3% interest compounded weekly, how long would she have to wait to see her investment turn into $5,000?
  1. Stacey invested $5,200 in a retirement account that pays 3% compounded monthly, at the age of 21. How much is her investment worth when she retires at the age of 59 1/2?
  1. A bank is offering Paul 1.5% in interest compounded quarterly. If he invested $3,000, how much will he earn after three years?