When Dan signed a two-year contract as a manager, the company allowed reimbursement of $470 at the end of every month for his car expenses. At the time the contract was signed, money was worth 9.63% compounded monthly (a) What value did the expense reimbursement provision have when the contract was signed? (b) What is the outstanding value of the reimbursement after the 12th payment? (a) The value was $ (Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) (b) The outstanding value is $ (Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Question

When Dan signed a two-year contract as a manager, the company allowed reimbursement of $470 at the end of every month for his car expenses. At the time the contract was signed, money was worth 9.63% compounded monthly (a) What value did the expense reimbursement provision have when the contract was signed? (b) What is the outstanding value of the reimbursement after the 12th payment? (a) The value was $ (Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) (b) The outstanding value is $ (Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

(a) To find the value of the expense reimbursement provision when the contract was signed, we can use the formula for the present value of a series of payments:

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

where PV is the present value, P is the monthly payment, r is the monthly interest rate, and n is the number of payments.

In this case, P = $470, r = 9.63% = 0.0963, and n = 24 (2 years * 12 months/year). Plugging in these values, we get:

PV = $470 * [(1 - (1 + 0.0963)^(-24)) / 0.0963]
= $470 * [0.763222 / 0.0963]
≈ $3,741.83

So the value of the expense reimbursement provision when the contract was signed is approximately $3,741.83.

(b) To find the outstanding value after the 12th payment, we can use the formula for the future value of a series of payments:

FV = P * [(1 + r)^n - 1] / r

where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of remaining payments.

In this case, P = $470, r = 9.63% = 0.0963, and n = 12 (24 payments in total - 12 payments already made). Plugging in these values, we get:

FV = $470 * [(1 + 0.0963)^12 - 1] / 0.0963
= $470 * [1.963222 - 1] / 0.0963
≈ $5,709.09

So the outstanding value of the reimbursement after the 12th payment is approximately $5,709.09.

Answer 2

To calculate the value of the expense reimbursement provision, we can use the formula for the future value of a series of monthly payments:

FV = PMT * ((1 + r)^n - 1) / r

Where:
FV = future value
PMT = monthly payment
r = monthly interest rate
n = number of payments

(a) To calculate the value when the contract was signed:

PMT = $470
r = 9.63% / 100 / 12 (monthly interest rate)
n = 2 years * 12 (number of payments in months)

PMT = $470
r = 0.0963 / 12
n = 2 * 12

FV = $470 * ((1 + 0.0963 / 12)^(2 * 12) - 1) / (0.0963 / 12)

Using a calculator, the value (a) is approximately $6,218.26 (rounded to the nearest cent).

(b) To calculate the outstanding value after the 12th payment:

PMT = $470
r = 9.63% / 100 / 12 (monthly interest rate)
n = 2 years * 12 (number of payments in months)
k = 12 (the 12th payment)

PMT = $470
r = 0.0963 / 12
n = 2 * 12
k = 12

FV = $470 * ((1 + 0.0963 / 12)^(2 * 12) - (1 + 0.0963 / 12)^12) / (0.0963 / 12)

Using a calculator, the outstanding value (b) is approximately $2,974.16 (rounded to the nearest cent).