Question

• 1) A new car is purchased and a $20,000 loan is taken. The loan is for 5 years (60 months) and the interest rate is 7.9% compounded monthly. What is the monthly payment? • 2)A new car is purchased and a $20,000 loan is taken. The loan is for 5 years (60 months) and the interest rate is 7.9% compounded monthly. What is the balance after 3 years? . 3) A new car is purchased and a $30,000 loan is taken. The loan is for 6 years (72 months) and the interest rate is 5.9% compounded monthly. a) What is the monthly payment? b) How much interest will be paid over the term of the loan? • 4) $10,000 is still owed on a car loan. The loan has an interest rate of 2.9% compounded monthly and calls for monthly payments. The current payment is $200 per month. How long will it take to pay the loan off? Round to the nearest month. • 5) Anthony can afford $250 per month for a truck payment. What size of a truck loan can he take if he plans to finance at: a) 6 years (72 months) at an interest rate of 6% compounded monthly? b) 5 years (60 months) years at an interest rate of 6% compounded monthly?

Answer 1

Hey there, hope this helps

1)

We will be using following formulae to calculate interest

A= P(1 + r/n)^nt

Then Monthly Interest= (A - P)/12*t

Where:

• A = Accrued Amount (principal + interest)
• P = Principal Amount
• I = Interest Amount
• R = Annual Nominal Interest Rate in percent
• r = Annual Nominal Interest Rate as a decimal
• r = R/100
• t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
• n = number of compounding periods per unit t; at the END of each period

Accrued Amount=9573.6 calculated by[(20000*(1+0.079/4)^20)-20000]

Monthly Interest=159.56 Calculated by [9573.6/60]

2) Balance after 3 years= 25290.33 calculated by [(20000*(1+0.079/4)^12)]

*Assuming that we have not paid anything yet against the loan.

3)Accrued amount=42705.6 calculated by [(30000*(1+0.059/12)^72)]

a) Monthly Payment =176.47 calculated by [(42705.6-30000)/72]

b) interest payment=12705.6 calculated by {42705.6-30000}

4)Time take to fully pay off loan(t)=4.8years calculated by {t=Log(200t/10000)/12log(1+(0.29/12))}

5)a)Principal Amount=3225 calculated by[(250*72)/(1+0.29/12)^72]

b)Principal Amount=3580 calculated by[(250*60)/(1+0.29/12)^60]

Best of luck.