RipOff Dealers, Inc. offers a financing plan for car purchases, charging 2% per month. If a car costs $30,000, what's the monthly payment you will have to make - starting a month from now - if you need 5 years to pay off the debt on the car?
Answer(s): C
The payments constitute an ordinary annuity. The present value of an n-period annuity that starts paying at the end of the current period equals PV = (C/r)*[1 - 1/(1+r)^n] where C is the payment per period and r is the one- period interest rate. In this example, the annuity is over 5*12 = 60 periods and the per period rate equals 2%.So the present value of the payments equals (C/0.02)*[1 - 1/1.02^60] = 30,000 (given). Solving for C gives the per month payment equal to $863.
If you buy an item for $500 and agree to pay for it with 24 monthly payments of $24.50, beginning next month, what annual interest rate, compounded monthly, are you being charged?
The interest rate returned by the calculator will be the periodic interest rate. It must be multiplied by the number of periods per year to have the correct answer. On the BAII Plus, press 24 N, 500 PV, 24.50 +/- PMT, 0 FV, CPT I/Y. Then press x 12 = to see the answer. On the HP12C, press 24 n, 500 PV, 24.50 CHS PMT, 0 FV, i.Then press 12 x to see the answer. Make sure the BAII Plus has the P/Y value set to 1.
A bank savings account offers a savings rate of 3.5% per year, compounded annually. How long would it take for an investment of $710 to grow to $1,000?
Answer(s): D
If it takes n years for the growth, then 1000 = 710*(1+3.5%)^n. Solving for n gives 9.96 years.
Assume you buy a computer for $1,350 and agree to pay for it with 24 payments of $45, beginning next month. What is the size of the final payment needed at month 24 to completely pay off the computer, if the interest rate you are being charged is 16% per year, compounded monthly?
Answer(s): E
This question describes a situation often called a balloon payment. On the BAII Plus, press 24 N, 16 divide 12 = I/Y, 1350 PV, 45 +/- PMT, CPT FV. On the HP12C, press 24 n, 16 ENTER 12 divide i, 1350 PV, 45 CHS PMT, FV. The answer is shown as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.
What amount would you have in your savings account in 5 years, if it has a balance of $1,234 today and you deposit an additional $1,234 two years from today? Assume that the savings account earns 5% per year, compounded annually.
Answer(s): B
Solve this question as two compound interest problems. The first $1,234 will be in the account for 5 years. The second $1,234 will be in the account for 3 years. Find the FV of both values 5 years from today and add them together. On the BAII Plus, press 5 N, 5 I/Y, 1234 PV, 0 PMT, CPT FV, which yields $1,574.93. Then press STO 1. Then press 3 N, CPT FV, which yields $1,428.51. Press + RCL 1 = to see the answer. On the HP12C, press 5 n, 5 i, 1234 PV, 0 PMT, FV. Then press STO 1. Then press 3 n, FV. Press RCL 1 + to see the answer.Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the P/Y value set to 1.
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