Question

Many credit card companies charge a compound interest rate of 1.8% per month on a credit card balance. Nelson owes $450 on a credit card. If he makes no purchases or payments, he will go deeper and deeper into debt. Which of the following sequences describes his increasing monthly balance?

Answer 1

The series of nelsons debt balance is 450, 466.34, 474.74, 483.28 ……. Option D is correct.

Solution:

Given, Many credit card companies charge a compound interest rate of 1.8% per month on a credit card balance.

Means each month the rate increases exponentially.

Nelson owes $450 on a credit card and makes no purchases or payments, he will get into debt in the following way:

`450 *(1.018)^(t) \text { Here t represents the time. }`

Because we know that, compound interest
`=\text { amount } *\left(1+\frac{\text { rate }}{100}\right)^{\text {time }}`

$450 was initial amount.

`\begin{array}{l}{450 *(1.018)^(1)=\$ 458.10 \text { is for the } 1 \mathrm{st} \text { month }} \\ {450 *(1.018)^(2)=\$ 466.34 \text { is for the } 2 \text { nd month. }} \\ {450 *(1.018)^(3)=\$ 474.74 \text { is for the } 3 \mathrm{rd} \text { month. }} \\ {450 *(1.018)^(4)=\$ 483.28 \text { is for the fourth month and so on. }}\end{array}`

Hence, the series of nelsons debt balance is 450, 466.34, 474.74, 483.28 …….

Thus option D is correct