Use the formula for present value of money to calculate the...

Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $25,000 after 10 years with an APR of 6% compounded quarterly. Round your answer to the nearest cent, if necessary.

Transcript

00:01 So the question was asked to find the present value that has to be invested to become the money to some particular value that is the future value after 10 years with the annual percentage rate of 6 percentage and it was given that this is compounded quarterly.

00:15 Now the equation or the present value, the formula for present value of money is nothing but present value is equal to i can write that formula as this is similar to the compound interest formula only.

00:28 So present value will be equal to the future value divided by future value divided by one plus can write this as one plus r by n whole raise to n into t so this is our equation and here this r is the rate of interest per point period so rate of interest per period and n is the n i can write as compounding period and t is the total time period so in the if you're talking about the given question it was given that the rate of interest or the apr was given as six percentage so this will be six percentage so in decimal six percentage will be 0 .6 because by 100 you would have tried so not 0 .6 0 .06 will be in decimals and in compounding period was given that this is compounded quarterly that is four times in a year so the compounding period will be 4 and time period will be it was given as 10 years so this will be 10 years this is the given values and the future value is given as feature value is given as 25 ,000 so this is very similar to the formula to find the compound interest so compound interest is nothing but the amount that it will be reaching is the the principal amount into one plus r by n whole raise to n into t so using this equation only we can make this below equation so we have to find the present value so i'm just substituting all the values present value is equal to future value divided by 1 plus r by n r was 0 .06 divided by n was 4 into 4 into 10 i can write and this value will be equal to 106 divided by 4 plus 1 whole raise to 40 and we have to divide that with 25 000 by that answer will be equal to 13 ,781 .588.

03:25 This will be our answer.

03:27 And in the question, it was told that we have to round this value to the nearest send...

Question

Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $25,000 after 10 years with an APR of 6% compounded quarterly. Round your answer to the nearest cent, if necessary.

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