Question

Tom has taken out a loan for college. He started paying off the loan with a first payment of $300. Each month he pays, he wants to pay back 1.05 times as the amount he paid the month before. Explain to Tom how to represent his first 24 payments in sigma notation. Then explain how to find the sum of his first 24 payments, using complete sentences. Find the sum of his first 24 payments. Explain why this series is convergent or divergent.

Answer 1

Using Sigma Notation, you could write out the expression like this
\[\sum_{m =1}^{24} 300 * 1.05^{1-m}\]
Since m, the number of months, starts at 1 (m=1) and goes all the way up to 24. For each month, he will pay 1.05 times as much as the previous month, which is why we have the exponent (1.05 ^ (1-m)), and the starting amount for the first month is 300.

In order to find the total payments, you could manually add all the parts for each of the 24 months, (300 + 300*1.05 + .... 300 * 1.05^23), but there may be a simpler way to figure that out.

When answering whether the series is "convergent" or "divergent", think about whether the numbers in the sequence "converge" by approaching towards a single value OR whether they "diverge" by growing bigger and bigger?

Answer 2

what would the confidence interval be

Answer 3

i got it thank you for the help.much appreciated!

Answer 4

Oh wonderful, that's great! Glad you figured it ou

Answer 5

\[\sum_{m=1}^{24}300(1.05)^{m-1}\]