I need help with these few questions on my homework please :)
1. How much money would you need to pay to receive a payout annuity of $8,503.05 annually for 10 years, assuming your money earns 7.5% compounded annually? Assume that your payments increase annually by a 3% COLA.
Answer___ Units___
2.You are purchasing a Yugo SUV for $9500. You have a downpayment of $800, and will finance the rest over 4 years at 9.0 % add-on interest. What is your monthly payment?
Answer___ Units___
3.You buy a car and need to finance $2,419 on a simple-interest amortised loan with 36 monthly payments and an interest rate of 5.2% . Find the monthly payment.
Answer___ Units___
Any help will help, thank you!
#1 is the interesting question
Since the annuity payments become your "salary", I will assume they are made at the beginning of the year.
IF x is the first payment made now , the Present Value is:
PV = 8,503.05 + (1.03)(1.075)^-1 (8,503.05) + (1.03)^2 (1.075)^-2 (8,503.05) + .... + (1.03)^9 (1.075)^-9 (8,503.05)
this is a geometric series with
a = 8,503.05
r = (1.03)(1.075)^-1 = .958139534
n = 10
PV = sum(10) = 8,503.05 (1 - .958139534^10)/(1 - .958139534)
= 70676.49
#2 A Yugo SUV ????
let the payment be x
8700 = x (1 - (1+.09/12)^-48)/(1+.09/12)
you do the button pushing
btw, What do you call a Yugo with two tailpipes?
A wheelbarrow .
#3. I have no idea what a "simple-interest amortised loan" is.
You probably have an example in your text or notes.
#3. amortized is if both the principal and interest rate are paid by a sequence of equal periodic payments
Amortization Formula:
R=monthly payments (?)
P= principal amount ($2419.)
i= 5.2% interest rate (0.052/36)
n = number of payments (36 months)
R = P(i)
-------
1-(1+i)^-n
R= (2419 * 0.052/36) / [1-(1-(0.052/35)]^-36
R= $72.72 monthly payments
Sure, I'd be happy to help you with your homework questions! Let's go through each question one by one and I'll explain how to find the answers.
1. To calculate the amount of money you would need to pay to receive a payout annuity, we can use the formula for present value of an annuity. The formula is:
PV = PMT / (1 + r)^n
Where PV is the present value, PMT is the payment amount, r is the interest rate, and n is the number of periods.
In this case, the payment amount is $8,503.05 annually, the interest rate is 7.5% compounded annually, and the number of periods is 10 years.
To account for the increasing payments with a 3% COLA, we can assume a constant growth rate of 3% in the formula. This means the payment in the first year is $8,503.05, the payment in the second year is $8,503.05 * (1 + 3%) = $8,754.14, and so on.
Using this information, we can calculate the present value as follows:
PV = $8,503.05 / (1 + 0.075)^1 + $8,754.14 / (1 + 0.075)^2 + ...
You would need to sum up the present values for each year, up to the 10th year, to get the total amount of money you would need to pay.
2. To calculate the monthly payment for a loan with add-on interest, we can use the formula:
MP = (PV + (PV * r * n)) / (n * t)
Where MP is the monthly payment, PV is the present value (loan amount), r is the interest rate, n is the number of periods per year, and t is the total number of years.
In this case, the present value is the amount you need to finance after the down payment, which is $9500 - $800 = $8700. The interest rate is 9.0% and the loan term is 4 years.
Plugging in these values into the formula, you can calculate the monthly payment.
3. To calculate the monthly payment for a simple interest amortized loan, we can use the formula:
MP = P / n
Where MP is the monthly payment, P is the principal amount (loan amount), and n is the number of payments.
In this case, the principal amount is $2,419 and the number of payments is 36. The interest rate is given as 5.2%, but since it's a simple interest loan, we don't need to use it in this calculation.
Simply divide the principal amount by the number of payments to find the monthly payment.
Now that I've explained how to solve each question, you can use the formulas and information provided to find the answers. Let me know if you need any further assistance!