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Gloria pays her insurance three times each year. The first payment is 40\(\%\) of the annual premium, and each of the next two payments is 30\(\%\) of the annual premium. If the annual premium is \(\$ 924,\) find the amounts of the three payments.

Short Answer

Expert verified
The amounts of Gloria's three payments are \$ 369.6 for the first payment and \$ 277.2 each for the next two payments.

Step by step solution

01

Calculate the first payment

The first payment equates to 40\(\%\) of the annual premium. We calculate this amount by multiplying the total annual premium, which in this case is \(\$ 924\), by 40\(\%\). The calculation would thus look like this: \(\$ 924 \times 0.40 = \$ 369.6\)
02

Calculate the subsequent payments

Each of the two subsequent payments equates to 30 \(\%\) of the annual premium. We calculate them in the same way, but instead use 30 \(\%\) for the calculations. This will be: \(\$ 924 \times 0.30 = \$ 277.2\)
03

Summarize the payments

The first payment Gloria makes is \$ 369.6, and both of the two subsequent payments are \$ 277.2 each.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Annual Premium
When discussing insurance, the term "annual premium" refers to the total amount of money paid for a policy over a period of one year. It is an important concept in understanding how your coverage is structured and how much it will cost you over the year.
In the problem above, Gloria's annual premium for her insurance is $924. This is the key figure from which all her payments are calculated. Understanding how this premium is divided across the year is essential. Typically, insurers allow you to pay this amount in one lump sum or through smaller, more manageable payments. These options might include semi-annual, quarterly, or even monthly payments. Here, Gloria pays her insurance in three installments, which is not as common as monthly or semi-annual payments, but still a feasible option.
Knowing your annual premium is crucial, as it helps you budget and plan your finances ahead of time, especially if you opt for staggered payments.
Insurance Payments
Insurance payments refer to the specific amounts paid to keep your insurance policy active. These payments can be made annually or split into smaller periods like monthly or quarterly installments.
Each payment you make goes toward the overall annual premium, ensuring your insurance coverage remains valid. For Gloria, this involves making one larger payment of 40% of her total premium and two smaller ones at 30% each.
Insurance payments are calculated as a percentage of your annual premium to simplify budgeting. For example, let's break down Gloria's payments:
  • First Payment: Calculated as 40% of $924, resulting in $369.6.
  • Subsequent Payments: Each is 30% of the annual amount, which equates to $277.2.
By spreading out these payments, you can manage finances more effectively and avoid the financial strain of a large lump sum payment.
Financial Problems
Managing insurance and its related payments can sometimes lead to financial problems if not properly budgeted. This is why understanding the breakdown of insurance payments is vital.
For individuals like Gloria, knowing exactly how much is due and when can prevent unexpected cash flow issues. For example, understanding that her first payment is slightly higher can help Gloria plan her finances accordingly. Here are some strategies to avoid financial problems with insurance payments:
  • Automatic Payments: Setting up automatic transfers to ensure payments are made on time.
  • Budgeting: Formulating a monthly budget that accounts for each scheduled payment.
  • Emergency Fund: Keeping a reserve for unexpected expenses, ensuring insurance payments are unaffected.
These measures can help you stay on top of your insurance liabilities, ensuring continuous coverage without financial stress.

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