Question

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.

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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!

Answer 1

#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.

Answer 2

#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