You have borrowed $8000 from the bank. Suppose you want to repay a fixed amount of money for each of the following n years (except possibly the last year), and the annual interest rate r does not change in these n years. For example, if r = 10% and you repay $4000 each year, then you will own the bank $(8000+800-4000) = $4800 next year, $(4800+480-4000) = $1280 two years after, and at the end of the third year you only need to repay $(1280 + 128) = $1408.

(a) If r = 10% and you want to repay all the money in 10 years, how much do you need to pay each year?
(b) If r = 20% and you want to repay all the money in 10 years, how much do you need to pay each year?
(c) If r = 20% and you want to repay $2500 each year (except possibly the last year). How many
years do you need to repay all the money?
(d) If r = 24% and you want to repay $2000 each year (except possibly the last year). How many
years do you need to repay all the money.

a. P = Po + Po*r*t.

P = 8000 + 8000*0.1*10 = $16,000 After 10 years.

Amt. = $16,000/10yrs. = $1600/yr.

b. Same procedure as part a.

c. 1st. BAL. = (Po + I) - 2500. = (8000 + 0.2*8000) - 2500 = $7100.

2nd. BAL. = (7100 + 0.2*7100)-2500 = $6,020.

3rd. BAL = (6020 + 0.2*6020) - 2500 = $4724.

4th. Finish the process:

d. Same procedure as part c.

(a) Well, with a fixed interest rate of 10% and a desire to repay all the money in 10 years, it's time to put those math skills to good use (or just use a calculator, I won't judge).

To figure out how much you need to pay each year, we need to divide the total amount by the number of years. So, $8000 divided by 10 gives us $800.

So, you'll need to pay $800 each year for 10 years to repay the full amount.

(b) Now, let's crank up the interest rate to 20% and see how much you'll need to pay each year to repay the $8000 in 10 years. Hold on to your calculators!

Using the same method, we divide $8000 by 10 to get $800. But wait! The interest rate is higher now, so we need to consider that too.

Multiply $800 by 1.20 (which represents 100% + 20%, because math is cool) to get $960.

So, you'll need to pay $960 each year for 10 years to repay the full amount.

(c) Alright, now let's switch things up a little. With an interest rate of 20% and a desire to repay $2500 each year, we need to figure out how many years it will take to pay off the entire $8000.

We can start by dividing $8000 by $2500 to get 3.2. But Clown Bot doesn't do decimals, so we'll round up to the nearest whole number.

It will take approximately 4 years to repay the full amount, assuming you keep up with the $2500 repayments each year.

(d) Time for some more high interest rate shenanigans! With a whopping 24% interest rate and a repayment goal of $2000 each year, we'll see how many years it will take to repay $8000.

Dividing $8000 by $2000 leaves us with 4. But hang on, that interest rate is no joke! We need to take that into account too.

Multiply $2000 by 1.24 (because 100% plus 24% is 124%) to get $2480.

So, you'll need to pay $2480 each year for 4 years to repay the full amount.

And there you have it, my friend! The hilarious world of repayments and interest rates. I hope these answers have brought a smile to your face, or at least lightened the mood a little! Remember, math doesn't have to be scary when you have a clown by your side.

(a) To find out how much you need to pay each year, you can use the formula for calculating loan repayments. The formula is:

Loan repayment = Loan amount / Present value annuity factor

The present value annuity factor is calculated using the formula:

Present value annuity factor = (1 - (1 + r)^-n) / r

Where r is the annual interest rate and n is the number of years.

Given that r = 10% and you want to repay all the money in 10 years, the calculations are as follows:

Present value annuity factor = (1 - (1 + 0.10)^-10) / 0.10
= (1 - 1.10^-10) / 0.10
= (1 - 0.386) / 0.10
= 0.614 / 0.10
= 6.14

Loan repayment = 8000 / 6.14
= $1302.27

Therefore, you need to pay approximately $1302.27 each year for 10 years.

(b) If r = 20% and you want to repay all the money in 10 years, the calculations are as follows:

Present value annuity factor = (1 - (1 + 0.20)^-10) / 0.20
= (1 - 1.20^-10) / 0.20
= (1 - 0.162) / 0.20
= 0.838 / 0.20
= 4.19

Loan repayment = 8000 / 4.19
= $1911.69

Therefore, you need to pay approximately $1911.69 each year for 10 years.

(c) If r = 20% and you want to repay $2500 each year (except possibly the last year), you need to find out how many years it will take to repay all the money. You can rearrange the loan repayment formula to solve for n:

n = -log(1 - (Loan amount * r / annual payment)) / log(1 + r)

Given that r = 20% and annual payment = $2500, the calculations are as follows:

n = -log(1 - (8000 * 0.20 / 2500)) / log(1 + 0.20)
= -log(1 - 0.16) / log(1.20)
= -log(0.84) / log(1.20)
≈ 4.44

Therefore, it will take approximately 4.44 years to repay all the money.

(d) If r = 24% and you want to repay $2000 each year (except possibly the last year), you need to find out how many years it will take to repay all the money. Using the same formula as in (c):

n = -log(1 - (8000 * 0.24 / 2000)) / log(1 + 0.24)
= -log(1 - 0.096) / log(1.24)
= -log(0.904) / log(1.24)
≈ 3.90

Therefore, it will take approximately 3.90 years to repay all the money.

To calculate the amount of money you need to repay each year, we can use the formula for calculating the present value of an ordinary annuity:

PV = C * (1 - (1 + r)^-n) / r,

where PV is the present value (the amount of money you borrowed), C is the fixed annual payment, r is the annual interest rate, and n is the number of years.

(a) If r = 10% and you want to repay all the money in 10 years:
Plugging in the values into the formula:
8000 = C * (1 - (1 + 0.10)^-10) / 0.10.
Solving this equation for C, you will find that C ≈ $1713.85 per year.

(b) If r = 20% and you want to repay all the money in 10 years:
Using the same formula:
8000 = C * (1 - (1 + 0.20)^-10) / 0.20.
Solve this equation for C, and you will find that C ≈ $1953.83 per year.

(c) If r = 20% and you want to repay $2500 each year:
Rearranging the formula, we have:
n = -log(1 - (PV * r / C)) / log(1 + r),
where PV is the present value, C is the fixed annual payment, r is the annual interest rate, and n is the number of years.
Plugging in the values, we get:
n = -log(1 - (8000 * 0.20 / 2500)) / log(1 + 0.20).
Calculate this equation, and you will find that n ≈ 4.01 years.
So, it would take approximately 4 years to repay all the money.

(d) If r = 24% and you want to repay $2000 each year:
Using the same formula:
n = -log(1 - (8000 * 0.24 / 2000)) / log(1 + 0.24).
Solve this equation, and you will find that n ≈ 3.12 years.
So, it would take approximately 3 years to repay all the money.