Question

money planning
part 1 of 3 1 2 3 trying to earn:
sybil ford has a checking account at township credit union on which she earns 3% interest annually. she buys a cabin with a loan. the interest rate on the loan is 12.5%, but she doesnt have to make any payments during the first year. then she will make monthly payments until the loan is paid off.
today, sybil has:

• a checking account with $25,000, which earns 3% interest annually
• $16,000 in cabin loan debt, with no payments the first year, but with the loan amount increasing by 12.5% at the end of the first year

today, the combined (
et\) value of these two accounts is $9000, which is the difference between the value of the checking account and the cabin loan debt (= $25,000 - $16,000).
question 1: according to the terms of her loan, sybil makes no payments on her cabin loan for the first year. she also makes no deposits or withdrawals from her checking account. at the end of the year, what will be the net value of the two accounts:
$
question 2: if, instead of getting a loan, sybil bought the cabin by using money from her checking account at the beginning of this year, what would the net value of the two accounts be at the end of the year:
$
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Explanation:

Step1: Calculate checking account value

The checking account earns 3% annual interest. The formula for the new value is initial value $\times (1 + \text{interest rate})$.
$\$25,000 \times (1 + 0.03) = \$25,000 \times 1.03 = \$25,750$

Step2: Calculate loan value after 1 year

The loan increases by 12.5% in the first year. The formula is initial loan $\times (1 + \text{interest rate})$.
$\$16,000 \times (1 + 0.125) = \$16,000 \times 1.125 = \$18,000$

Step3: Find net value for Q1

Net value is checking account value minus loan value.
$\$25,750 - \$18,000 = \$7,750$

Step4: Calculate new checking account for Q2

Sybil uses $\$16,000$ from her $\$25,000$ checking account, so the initial balance becomes $\$25,000 - \$16,000 = \$9,000$. This earns 3% annual interest.
$\$9,000 \times (1 + 0.03) = \$9,000 \times 1.03 = \$9,270$

Step5: Find net value for Q2

There is no loan, so net value equals the checking account value.
$\$9,270 - \$0 = \$9,270$

Answer:

Question 1: $\$7,750$
Question 2: $\$9,270$