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Answer :
Final answer:
The initial value in Tim's situation is $;125, which was the upfront payment made at the time of purchase before the installment payments of $50 per month. Initial value can refer to down payments in various financial scenarios, such as buying a new item, making real estate transactions, or calculating the terms of a loan agreement.
Explanation:
The initial value in this situation where Tim bought a new item for $125 and then paid $50 per month until it was fully paid off refers to the upfront payment made at the time of the purchase. Therefore, the initial value is $125. This is a common payment structure in which a larger sum is paid initially, followed by smaller, regular payments over time. Tim's transaction comprises an initial payment (a down payment of sorts) and the subsequent $50 payments are part of the installment plan or amortization of the total cost of the item.
In finance, understanding initial values, interest, and total future amount calculations is essential. For example, when discussing simple interest, which for the sake of an illustrated example is $5, one would calculate the future amount using a specific formula. Additionally, when considering scenarios such as real estate transactions, the initial value could be the down payment or cash offer on a property. Continuing with the illustration, if Freda bought a house for $150,000 in cash (initial value), it would sell for $250,000, showing an increase in value. Similarly, Ben's initial value in his transaction is the 20% down payment on a $100,000 house, which excludes the amount borrowed from the bank. For complex financial structures like mortgages, monthly payments are calculated and can differ based on the payment amount. For instance, given the example, a monthly payment of $1,798.65 paid over 30 years totals $647,514.57, which is more than twice the original loan amount (initial value).
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