Final answer:
The equivalent payments that would settle the debt at different times can be found using the present value formula. The equivalent payment now would be the full amount of $2800. In 3 years, the equivalent payment would be approximately $2474.42. In 6 years, the equivalent payment would be approximately $2188.67. In 12 years, the equivalent payment would be approximately $1808.31.
Step-by-step explanation:
To find the equivalent payments that would settle the debt at different times, we can use the present value formula. The present value formula calculates the value of an amount of money at a specific point in time, given a certain interest rate. The formula is:
PV = C/(1+r)^n
Where PV is the present value, C is the future amount to be received or paid, r is the interest rate, and n is the number of periods
(a) Now:
Since the loan is due now, the equivalent payment would be the full amount of $2800.
(b) In 3 years:
To calculate the equivalent payment in 3 years, we can use the formula:
PV = C/(1+r)^n
Where C is the future amount of $2800, r is the interest rate of 4.2%, and n is the number of periods which is 3 years.
Plugging in the values, we get:
PV = 2800/(1+0.042)^3
Calculating the equation, the equivalent payment in 3 years would be approximately $2474.42.
(c) In 6 years:
Using the formula PV = C/(1+r)^n, where C is $2800, r is 4.2%, and n is 6 years, the equivalent payment in 6 years would be:
PV = 2800/(1+0.042)^6
Calculating the equation, the equivalent payment in 6 years would be approximately $2188.67.
(d) In 12 years:
Similarly, using the formula PV = C/(1+r)^n, where C is $2800, r is 4.2%, and n is 12 years, we can find the equivalent payment in 12 years:
PV = 2800/(1+0.042)^12
Calculating the equation, the equivalent payment in 12 years would be approximately $1808.31.