Question

Ohn has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he paid the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of his first 20 payments, using complete sentences.

Answer 1

Answer:

Ohn has paid $5730 in first 20 installments

Step-by-step explanation:

As per the question Ohn payed the first installment =$100

Next month Ohn payed the installment = 1.1×$100

Similarly subsequent installment =1.1×1.1×$100

So we can write first 20 installments as

⇒100+100×1.1+100×1.1²+100×1.1³.........+100×$1.1^{20}$

And we know in geometric series

1+x²+x³+...........$x^{20}$ = (1-$x^{n-1}$)÷(1-x)

Therefore sum of first 20 installments will be

⇒100(1+1.1²+1.1³............$1.1^{20}$ =(1- $1.1^{20}$)÷(1-1.1)

= 100(1-6.73)÷(-.1)

=100×5.73÷.1

= $5730

So Ohn has paid $5730