Question

Answer all please

1.Allysha just borrowed 48,100 dollars. She plans to repay this loan by making a special payment of 5,200 dollars in 3 years and by making regular annual payments of 6,700 dollars per year until the loan is paid off. If the interest rate on the loan is 9.99 percent per year and she makes her first regular annual payment of 6,700 dollars in one year, then how many regular annual payments of 6,700 dollars must Allysha make? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

2.

Brenna wants to buy a car that is available at two dealerships. The price of the car is the same at both dealerships. Best Buggies would let her make quarterly payments of $2,250 for 5 years at a quarterly interest rate of 3.82 percent. Her first payment to Best Buggies would be due immediately. If California Cars would let her make equal monthly payments of $920 at a monthly interest rate of 1.35 percent and if her first payment to California Cars would be in 1 month, then how many monthly payments would Brenna need to make to California Cars?  Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

3.

Aldo wants to borrow $12,000 from the bank and is choosing among two possible loans. The interest rate on both loans is 1.4 percent per month. Loan A would require him to make 60 equal monthly payments, with the first payment made to the bank in 1 month. Loan B would also require him to make equal monthly payments to the bank. However, 1) the monthly payment associated with loan B would be $30 less than the monthly payment associated with loan A, and 2) the first monthly payment for loan B would be made to the bank later today. How many monthly payments to the bank must be made with loan B? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

4.

Celeste just borrowed 41,300 dollars. She plans to repay this loan by making equal quarterly payments of 3,327.52 dollars for 16 quarters. If she makes her first quarterly payment later today, then what is the quarterly interest rate on the loan? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

1) Amount borrowed by Allysha = $48100

Amount paid in 3rd year = $5200

Present value of amount paid in 3rd year = 5200/ (1+r)^n

                                                                 = 5200/ ( 1.0999)^3

                                                                 = $3907.90

PV is given by formula, PV = C * {1-( 1+R)^-N}/ R

Here value of loan is equal to presnt value of all the future payment made discounted at 9.99 %.

48100 = 3907.9 + 6700 *{ 1-( 1.0999)^ -N}/ R

            44192 = 67067.07 *{1-(1.0999)^- N}

            44192/67067.07 = {1-( 1.0999)^ - N)}

           .6589 = { 1 - ( 1.0999)^ -N}

           N = 5.32 years

Allysa has to make 5.32 annual payments of 6700 USD to repay the loan amount.

2) The price of the car is the PV of the payments made for the car in the future discounted at the interest rate .

PV = 2250 + 2250* { 1- ( 1+ .0382) ^ - 19 }/.0382

     =2250 + 2250 * { 1- .4925}/.0382

   =2250 + 13.2853*2250

= $32141

No of monthly payment to California cars can be derived from formula for PV.

32141 = 920 * { 1- ( 1+ .0135)^ -N}/ .0135

32141/920 = {1-(1+ .0135) ^ - N } / ,0135

.4716 = { 1- ( 1+ .0135) ^ -N}

N = 28.81 months

4) The rate of interest can be found out using help of formula of PV for annuity,

Let r be the rate of interest.

         41300 = 3327.52 + 3327.52 *{1-(1+r)^-15} / r

      (41300 -3327.52 )/3327.52 = { 1- ( 1+r) ^ - 15}/r

            11.41 = {1- ( 1+r) ^ - 15 } / r

                 r = 3.63 % compounded quarterly.