- Anurag is buying a house for $100,000 and needs a mortgage loan. Bank A wants him to repay the loan in 240 months with monthly payment of $600.72. Bank B wants him to repay the loan in 360 months with a monthly payment of 389.94. Which bank should he choose? Explain.
- Kwane and Karen each deposited $2000 in saving accounts. Kwane's bank pays 3.1% simple interest. Karen bank's pays 2.7% interest compounded annually. Which account will earn more interest in 3 years? Show your work.
Oh, the world of mortgages and savings accounts! Let me put on my jester hat and help you figure this out.
For the mortgage question, let's crunch some numbers and see which bank Anurag should choose.
Bank A: Monthly payment of $600.72 for 240 months.
Bank B: Monthly payment of $389.94 for 360 months.
To find out which bank is better, we need to calculate the total amount paid over the term of the loan. Let's do the math, but fear not, I'll make it fun!
Bank A: 600.72 * 240 = $144,172.80
Bank B: 389.94 * 360 = $140,378.40
Seems like Bank B is the winner here! Anurag will end up paying less over the term of the loan. Plus, as a bonus, he gets some extra clown jokes for free!
Now, let's dive into the Kwane and Karen savings account conundrum. I promise this won't make you feel like you're juggling numbers!
Kwane's bank offers 3.1% simple interest, while Karen's bank compounds interest annually at a rate of 2.7%. We want to find out who will earn more interest in 3 years:
Kwane's account: $2000 * 3.1% * 3 years = $186
Karen's account: $2000 * (1 + 0.027)^3 - $2000 = $162.16
Looks like Kwane's account wins this round! He'll earn $186 in interest compared to Karen's $162.16. I hope this helped lighten up the financial situation for you!
1. To determine which bank Anurag should choose, we need to compare the total amount repaid for each loan option.
For Bank A:
- Loan amount: $100,000
- Loan term: 240 months
- Monthly payment: $600.72
Total repayment for Bank A: 240 months * $600.72 = $144,172.80
For Bank B:
- Loan amount: $100,000
- Loan term: 360 months
- Monthly payment: $389.94
Total repayment for Bank B: 360 months * $389.94 = $140,378.40
From the calculations, we can see that Bank B requires a lower total repayment amount. Therefore, Anurag should choose Bank B because it offers a more favorable loan option.
2. To determine which account will earn more interest in 3 years, we need to calculate the interest earned for each account.
For Kwane's account:
- Principal amount: $2000
- Interest rate: 3.1%
- Time period: 3 years
Interest earned for Kwane's account: $2000 * 3.1% * 3 years = $186.00
For Karen's account:
- Principal amount: $2000
- Interest rate: 2.7%
- Time period: 3 years
Interest earned for Karen's account is compounded annually, so we need to use the compound interest formula:
Compound interest = Principal * (1 + interest rate)^time period - Principal
Interest earned for Karen's account: $2000 * (1 + 2.7%)^3 - $2000 = $165.36
From the calculations, we can see that Kwane's account will earn more interest in 3 years.
- To determine which bank Anurag should choose, we need to compare the total cost of the loan from each bank.
For Bank A:
Loan amount: $100,000
Loan term: 240 months
Monthly payment: $600.72
Total cost of the loan = Monthly payment * Loan term = $600.72 * 240 = $144,172.80
For Bank B:
Loan amount: $100,000
Loan term: 360 months
Monthly payment: $389.94
Total cost of the loan = Monthly payment * Loan term = $389.94 * 360 = $140,378.40
Comparing the total cost of the loan, Anurag should choose Bank B as it offers a lower total cost of the loan compared to Bank A. This means he will save money in the long run.
- To determine which account will earn more interest in 3 years, we can calculate the interest earned in each account using the given interest rates.
For Kwane's account:
Principal amount: $2000
Interest rate: 3.1%
Time: 3 years
Simple interest earned = Principal amount * Interest rate * Time = $2000 * 0.031 * 3 = $186
For Karen's account:
Principal amount: $2000
Interest rate: 2.7%
Time: 3 years
Compounding: Annually
Interest earned = Principal amount * (1 + Interest rate) ^ Time - Principal amount = $2000 * (1 + 0.027) ^ 3 - $2000 = $165.82
Comparing the interest earned, Kwane's account will earn more interest in 3 years as the simple interest of $186 is higher than the compounded interest of $165.82.