You have $400,000 saved for retirement. Your account earns 4% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years? $__.

You want to buy a $30,000 car. The company is offering a 5% interest rate for 60 months (5 years). What will your monthly payments be? $___.

A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $111,000.00 for 26 years at 6.3% compounded monthly, and will make monthly payments of $724.10. (Round all answers to 2 decimal places.)

           a) What is the unpaid balance after 14 months? $___.

           b) During this time period, how much interest did she pay? $___.

 

You owe $27,000 on student loans at an interest rate of 5.6% compounded monthly. You want to pay off the loan in 10 years.

           a) What will your monthly payments be? $___.

           b) How much interest do you pay? $___.

You want to buy a $135,000 home. You plan to pay 15% as a down payment and take out a 30 year loan at 4.6% interest for the rest.

           a) How much is the loan amount going to be? $___.

           b) What will your monthly payments be? $___.

           c) How much of the first payment is interest? $___.

1. $2,423.92
2. $566.14
3. a. $215,781.80, b. $5,156.63
4. a. $294.36, b. $8,323.20
5. a. $114,750, b. $588.26, c. $269.51

Step-by-step explanation

Please see attached picture for the solution.

To solve all of these set of problems, I used the formula for Ordinary Annuity for Present Value.

P = A[(1+i)ⁿ - 1] / i(1 + i)ⁿ

where

P = Present Value

A = Annuity or Amount per period

i = effective or real interest = r/m

n = total period = mt

t = duration (in years)

m = no. of compounding frequency in a year

Here, we will apply the formula for all the problems.

1. For the first question, it is required to determine the amount that can be pulled out in a bank monthly for 20 years at a rate of 4%. So, use the formula given above to solve for A. Directly substitute the given values. Note that m = 12 because the Annuity is will be withdraw monthly or 12 times in a year. You can now compute for the possible monthly withdrawal.
2. Just like in the first question, directly substitute the given values on the formula given above for Ordinary Annuity for Present Value. The monthly payment (A) will now be computed. Note that it is again monthly, so m = 12.
3. In the third question, for (a) it is asked for the balance left after 14 months. Since, P and A are all given, we do not need to use the formula for Ordinary Annuity. To compute for the balance after 14 months, Take the difference of total amount needed to pay for 26 years and total amount needed to pay for 14 months. For (b), use the formula given on the solution to get the interest at 14 months.
4. For (a), use the formula for Ordinary Annuity for Present Value to get the monthly payment (A). For (b), simply get difference of the total amount will be paid for 10 years and the amount borrowed.
5. For (a), it is stated that you will pay for 15% down payment for $135,000 home. So simply get the amount left after you paid 15% on which you will pay for 30 years. Now for (b), use the formula for Ordinary Annuity for Present Value considering the P as the amount left after you paid 15% down payment. For (c), use the formula given in the solution to get the interest at the first payment (n = 1 month).

Please use this google drive link to download the answer file.                                

https://drive.google.com/file/d/1mBxEZfji9iqrGwEpqKKiHxQjuCTWW0Pz/view?usp=sharing                                

Note: If you have any trouble in viewing/downloading the answer from the given link, please use this below guide to understand the whole process.                                
                                
https://helpinhomework.org/blog/how-to-obtain-answer-through-google-drive-link