Math 104 (Finance Review) Fall 2018 Name Payments: Walking through the mall, you

Question

Math 104 (Finance Review) Fall 2018 Name Payments: Walking through the mall, you spot a boat that you would like to own. The advertisement is claiming a low monthly payment. The terms ofthe payment are: 10% down, 180 months, 4.75% interest. The selling price of the boat is $26,690. Complete below. 1. a. What is the down payment amount D? D Formula needed for this situation: b. How many years is the boat to be financed? t c. What is the monthly payment advertised? R Formula needed for this situation: d. If all payments are made, what is the total finance charge of the loan? Formula needed for this situation (round to the nearest dollar) Total Finance Charge- Hint: Multiply the payment R by the total number of payments made m-t to find the total amount sent to the bank to pay back the money borrowed. Now, subtract the principal P (loan amount) from this to determine the cost of borrowing the money

Explanation / Answer

Question 1:

Down payment = 10% of the price of the boat = 0.10*26,690 = 2,669

Principal( P) = 26,690 -2,669 = 24,021

rate of interest (r) = 4.75% annually or 4.75%/12 (Monthly)

time period in years (t) = 180/12 =15 years

time period in months (m) =180 months

a) Down payment =10% of the price of the boat = 0.10*26,690 = 2,669

b) Number of years the boat is to be finance = 15 years

c) Monthly Payment (R) can be calculated using the PV of an annuity formula

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

24,021 = P*(1-(1+0.0475/12)^-180/ (0.0475/12)

24,021 = P*128.5624795

P = 186.843

Monthly payment (R) = $186.84

d) Finance charge = Monthly payment * number of payments - loan amount = 186.843*180-24,021 = 9,610.74

Finance change = $9,610.74

Question 2:

a.The future value of the annuity = P*((1+r)^n-1)/r = 186.843*((1+0.0475/12)^180 -1)/ (0.0475/12) = 48,859.61

Future value of the annuity = $48,859.61 (Rounded to nearest penny)

b. the future value of the single down payment is : FV = P*(1+r)^n = 2669*(1+0.0475/12)^180 = 5,434.66

Account balance 15 years = $5,435 (Rounded to nearest dollar)

c. Total amount = 5434.66 +48,859.61 = 54,294.27 = $54,294

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