Answer: A. To find the amount of the annual payment, we first need to calculate the total amount of the loan proceeds. Since they want a $25,000 advance at loan origination, the remaining loan proceeds are:
$350,000 - $25,000 = $325,000
The annual payment can be calculated using the present value of an annuity formula:
PMT = PV * r / (1 - (1 + r)^(-n))
Where PMT is the annual payment, PV is the present value of the loan proceeds, r is the interest rate per period, and n is the number of periods.
For this problem, r = 6% / 1 = 0.06 (since the interest rate is an annual rate and the payments are annual), n = 10 (since the term is ten years), and PV = $325,000.
Substituting these values into the formula, we get:
PMT = $325,000 * 0.06 / (1 - (1 + 0.06)^(-10)) = $39,199.96
Therefore, the amount of the annual payment is $39,199.96.
B. To find their interest charge in year 3, we need to first calculate the balance due at the beginning of year 3. To do this, we need to calculate the balance due at the end of year 2 and then add the interest for year 3. The balance due at the end of year 2 can be calculated using the future value of an annuity formula:
FV = PMT * ((1 + r)^n - 1) / r
Where FV is the future value of the annuity, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.
For this problem, r = 6% / 1 = 0.06, n = 2 (since we want to calculate the balance due at the end of year 2), and PMT = $39,199.96.
Substituting these values into the formula, we get:
FV = $39,199.96 * ((1 + 0.06)^2 - 1) / 0.06 = $86,977.25
Therefore, the balance due at the beginning of year 3 is $86,977.25. The interest charge for year 3 is simply the balance due at the beginning of year 3 multiplied by the interest rate:
Interest charge = $86,977.25 * 0.06 = $5,218.64
Therefore, their interest charge in year 3 is $5,218.64.
C. To find the total interest they pay if they hold the loan for its full term of ten years, we can use the total interest formula:
Total interest = PMT * n - PV
Where PMT is the annual payment, n is the number of periods, and PV is the present value of the loan proceeds.
For this problem, PMT = $39,199.96, n = 10, and PV = $325,000.
Substituting these values into the formula, we get:
Total interest = $39,199.96 * 10 - $325,000 = $66,999.60
Therefore, their total interest paid over the ten-year term is $66,999.60.
D. To find the balance due if they decide to repay the loan at the end of year 4, we can calculate the balance due at the beginning of year 5 and then subtract the annual payment for years 5-10. The balance due at the beginning of year 5 can be calculated
Wow this took a lot of typing