Final answer:
To find the interest rates earned in different scenarios, we can use formulas based on the initial and final amounts. (a) The interest rate earned when borrowing $690 and paying back $759 after 1 year is 10%. (b) The interest rate earned when lending $690 and receiving $759 after 1 year is also 10%. (c) The interest rate earned when borrowing $97,000 and paying back $464,106 after 15 years is 378%. (d) The interest rate earned when borrowing $12,000 and making annual payments of $2,771.70 for 5 years is 32%.
Step-by-step explanation:
(a) To find the interest rate earned when borrowing $690 and promising to pay back $759 at the end of 1 year, we can use the formula: Interest = Final amount - Initial amount. In this case, the interest would be $759 - $690 = $69. To calculate the interest rate, we can use the formula: Interest rate = (Interest / Initial amount) x 100. Plugging in the values, we get: Interest rate = ($69 / $690) x 100 = 10%.
(b) To find the interest rate earned when lending $690 and receiving $759 at the end of 1 year, we can use the same formula. The interest would be $759 - $690 = $69. Plugging in the values, we get: Interest rate = ($69 / $690) x 100 = 10%.
(c) To find the interest rate earned when borrowing $97,000 and promising to pay back $464,106 at the end of 15 years, we can use the same formula. The interest would be $464,106 - $97,000 = $367,106. Plugging in the values, we get: Interest rate = ($367,106 / $97,000) x 100 = 378%.
(d) To find the interest rate earned when borrowing $12,000 and making payments of $2,771.70 at the end of each year for 5 years, we can use the formula: Interest = Total payments - Initial amount. In this case, the interest would be ($2,771.70 x 5) - $12,000 = $3,858.50. To calculate the interest rate, we can use the formula: Interest rate = (Interest / Initial amount) x 100. Plugging in the values, we get: Interest rate = ($3,858.50 / $12,000) x 100 = 32%.