Lesson 3: Compound Interest (Present Value) Part A Définitions/Introduction Present Value: the principal that would have to be invested or borrowed NOW, today, to get a specific future value in a certain amount of time When people invest money they have a goal for which they want a specific amount of money. ( ex. for a trip, education, buying a house or car etc.) Part B Formula to Calculate Present Value We can calculate the present value that will result in a specific amount by using another form of the formula A = P(1 + i)n. We just isolate for P, but we use PV, present value, instead of P, since P is used for principal. Therefore to calculate present value we use: PV = —A_ ~ R PV =AQ1+i)" (1+1) Where: PV is the present value A is the accumulated amount i is the interest rate per compounding period n is the number of compounding periods Part C Examples Example 1: Determine the amount of money that must be invested today at 5% per annum, compounded semi-annually in order to have $1 000 available 6 years from now.
Example 3: Pia wants to borrow some money to start a new business but doesn't want it to be more than $25 000. Her bank will charge her interest at 5.3%/a compounded monthly. Pia wants to repay the loan in 4 years. What is the maximum amount that she can borrow and how much interest will she pay if she doesn't pay anything back until the end of the four years? 4-12=48 25000+48=520 57053%=27 27-48+25000 =$26325 Example 4: Karl is investing $7 000 that he would like to grow to at least $60 000 by the time he retires in 38 years. What annual interest rate, compounded semi-annually, will provide this? Round your answer to two decimal places.
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