MC algo 5-11 Calculating Annuity Present Values
Todd can afford to pay $335 per month for the next 5 years in order to purchase a new car. The interest rate is 5.7 percent compounded monthly. What is the most he can afford to pay for a new car today?
a. $17,453.72
b. $17,201.63
c. $16,581.04
d. $23,193.64
e. $18,035.51
To calculate the present value of the annuity, we can use the formula:
PV = PMT * [1 - (1 + r)^(-n)] / r
Where:
PV = present value
PMT = payment per period
r = interest rate per period
n = number of periods
In this case, Todd can afford to pay $335 per month for 5 years, so PMT = $335, n = 5 years * 12 months/year = 60 months, and r = 5.7% / 12 months = 0.475% per month.
Plugging in these values into the formula:
PV = $335 * [1 - (1 + 0.475%)^(-60)] / 0.475%
PV ≈ $16,581.04
Therefore, the most Todd can afford to pay for a new car today is approximately $16,581.04.
The correct option is c. $16,581.04.
To calculate the present value of an annuity, we can use the formula:
PV = PMT * ((1 - (1 + r)^(-n)) / r)
Where:
PV = Present Value
PMT = Payment per period
r = Interest rate per period
n = Number of periods
In this case, the payment per period (PMT) is $335, the interest rate per period (r) is 5.7% compounded monthly, and the number of periods (n) is 5 years.
First, we need to convert the annual interest rate to a monthly interest rate:
Monthly Interest Rate = (1 + Annual Interest Rate)^(1/12) - 1
Monthly Interest Rate = (1 + 0.057)^(1/12) - 1
Monthly Interest Rate = 0.004697737
Now, we can plug the values into the formula:
PV = $335 * ((1 - (1 + 0.004697737)^(-60)) / 0.004697737)
PV = $17,201.63
Therefore, the most he can afford to pay for a new car today is $17,201.63.
The correct answer is option b. $17,201.63.