a homeowner is financing the cost of new windows. two lenders have approved the homeowner for a $12,000…

a homeowner is financing the cost of new windows. two lenders have approved the homeowner for a $12,000 loan. the terms of each loan are: offer 1: 4.5% annual simple interest, with a total account balance of $14,430 after a 54 - month term offer 2: 3.75% annual interest compounded monthly for a balance of $14,430 after a 66 - month term assuming no payments are made, what is the difference in the account balances at the end of the loan terms. round your answer to the nearest penny. $204.88 $313.98 $767.12 $795.34

a homeowner is financing the cost of new windows. two lenders have approved the homeowner for a $12,000 loan. the terms of each loan are: offer 1: 4.5% annual simple interest, with a total account balance of $14,430 after a 54 - month term offer 2: 3.75% annual interest compounded monthly for a balance of $14,430 after a 66 - month term assuming no payments are made, what is the difference in the account balances at the end of the loan terms. round your answer to the nearest penny. $204.88 $313.98 $767.12 $795.34

Answer

Explanation:

Step1: Analyze Offer 1

The total account balance for Offer 1 is already given as $14,430 after a 54 - month term.

Step2: Analyze Offer 2

Use the compound - interest formula $A = P(1+\frac{r}{n})^{nt}$, where $P=$12000$, $r = 0.0375$ (3.75% annual interest rate), $n = 12$ (compounded monthly), and $t=\frac{66}{12}=5.5$ years. $A = 12000(1+\frac{0.0375}{12})^{12\times5.5}$ $A = 12000(1 + 0.003125)^{66}$ $A = 12000\times(1.003125)^{66}$ $(1.003125)^{66}\approx1.21836$ $A=12000\times1.21836=$14620.32$

Step3: Calculate the difference

The difference in account balances is $14620.32−14430=$190.32$

Answer:

None of the provided options are correct. The correct difference is $$190.32$