Mike wants to buy a snowmobile. His parents decide to lend him $9 000 at 10%/a, compounded monthly, if he agrees to repay the amount by making equal monthly (at the end of the month) payments for five years.
d. Write the series that represents the present value of the annuity.
e. Find the monthly payment using the formula.
f. Find the monthly payment using the T1 - 83 plus calculator. In your answer, include the values you entered for each parameter in TVM solver.
d)
i = .10/12 = .008333..
PV = 9000
= x(1.008333)^-1 + x(.008333)^-2 + ... + x(1.008333)^-60
e)
9000 = x[1 - 1.008333^-60]/.083333
9000 = x(47.0654126)
x = 191.22
f) that's all yours, I don't have one of those.
Thanks a million!
d. The series that represents the present value of the annuity can be calculated using the formula:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of monthly payments.
In this case, Mike wants to borrow $9,000, and he will make equal monthly payments for five years, which is a total of 60 months. The annual interest rate is 10%, compounded monthly. To find the monthly interest rate, we need to divide the annual interest rate by 12.
r = 10% / 12 = 0.10 / 12 = 0.00833
Now, we can substitute the values into the formula:
PV = PMT * [(1 - (1 + 0.00833)^(-60)) / 0.00833]
e. To find the monthly payment, we can rearrange the formula from part d to solve for PMT:
PMT = PV / [(1 - (1 + r)^(-n)) / r]
Substituting the given values:
PMT = $9,000 / [(1 - (1 + 0.00833)^(-60)) / 0.00833]
f. To find the monthly payment using a TI-83 Plus calculator, we can use the TVM Solver.
1. Press the APPS button.
2. Select "Finance" from the menu.
3. Choose option 1, "TVM Solver."
4. Enter the following values:
- N = 60 (number of payments)
- I% = 10 (annual interest rate)
- PV = -9000 (negative since it is a loan)
- FV = 0 (assuming no future value at the end of the loan)
- PMT = ? (unknown, to be calculated)
5. Leave the cursor on the PMT field and press ALPHA + ENTER to compute the monthly payment.
The calculator will display the monthly payment, along with any other relevant information such as the future value if applicable.