Question

Find the value on January 1, 2005 of quarterly payments of $100 for 10 years. The first payment is on 1/1/2007 and interest is 7% compounded quarterly.

solve the problem in a detailed way, writing a sentence of why you used each method you used

Answer 1

To find the value on January 1, 2005 of quarterly payments of $100 for 10 years with a 7% interest rate compounded quarterly, multiply the future value of one payment by the total number of payments. The value on January 1, 2005 of quarterly payments of $100 for 10 years is $6229.44.

Step-by-step explanation:

To find the value on January 1, 2005 of quarterly payments of $100 for 10 years with an interest rate of 7% compounded quarterly, we need to calculate the future value of each payment and then sum them up.

First, let's calculate the future value of one payment using the compound interest formula:

Future Value = Payment x ((1 + Interest Rate/Number of Compounding Periods)^(Number of Compounding Periods x Number of Years))

For each payment, the future value is $100 x ((1 + 0.07/4)^(4 x 10))

future value = $100 x (1.0175)^(40)

future value = $100 x (1.947016)

future value = $194.70.

Next, let's find out how many payments were made from January 1, 2007 to January 1, 2005. There are 8 years between these dates, and the payments are made quarterly, so there are 8 x 4 = 32 payments.

Now, let's calculate the total value by multiplying the future value of one payment by the total number of payments:

Total Value = Future Value of One Payment x Number of Payments = $194.70 x 32

Total Value = $6229.44

Therefore, the value on January 1, 2005 of quarterly payments of $100 for 10 years is $6229.44.