Question

A loan payment is made such that the first payment is $5 and each subsequent payment is 10% more than the previous. If the sum of payments made is $3,263, determine the number of loan payments made.

Answer 1

To determine the number of loan payments made, set up an equation based on the given information. The equation is solved to find the number of payments.

Step-by-step explanation:

To determine the number of loan payments made, we can set up an equation based on the given information. Let's denote the number of payments as 'n'. The first payment is $5, and each subsequent payment is 10% more than the previous. So, the second payment will be $5 + 10% of $5, the third payment will be $5 + 10% of the second payment, and so on.

Now, we can write the equation:

$5 + ($5 + 0.10($5)) + ($5 + 0.10($5 + 0.10($5))) + ... + ($5 + 0.10($5 + 0.10($5 + ...)))) = $3,263

Simplifying the equation, we have:

$5 + 1.10($5) + 1.10^2($5) + ... + 1.10^(n-1)($5) = $3,263

Using the formula for the sum of a geometric series, we can rewrite the equation as:

$5(1 - 1.10^n) / (1 - 1.10) = $3,263

Solving for 'n', we get:

1.10^n = ($3,263 x 0.10) / $5 + 1

n ln(1.10) = ln(($3,263 x 0.10) / $5 + 1)

n = ln(($3,263 x 0.10) / $5 + 1) / ln(1.10)

Calculating this equation will give us the number of loan payments made.