Answer:
The amount a bank will be willing to loan at an interest rate of 10% per year is $2,678,795.44.
Step-by-step explanation:
This can be calculated using the following 2 steps:
Step 1: Calculation of the present value of the loan in year 2
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV2 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV2 = Present value of the loan in year 2 =?
P = Annual payment = $400,000
r = Interest rate = 10%, or 0.10
n = number of years to make payments beginning in year 2 and ending in year 15 = 14
Substitute the values into equation (1) to have:
PV2 = $400,000 * ((1 - (1 / (1 + 0.10))^14) / 0.10)
PV2 = $400,000 * 7.3666874569392
PV2 = $2,946,674.98
Step 2: Calculation of the present value of the loan in year 1 or the amount a bank will be willing to loan at an interest rate of 10% per year
This can be calculated using the simple present value formula as follows:
PV1 = PV2 / (1 + r)^n ......................................... (2)
Where;
PV1 = Present value of the loan in year 1 = ?
PV2 = Present value of the loan in year 2 = $2,946,674.98
r = Interest rate = 10%, or 0.10
n = number of year = 1
Substitute the values into equation (2) to have:
PV1 = $2,946,674.98 / (1 + 0.10)^1
PV1 = $2,946,674.98 / 1.10
PV1 = $2,678,795.44
Therefore, the amount a bank will be willing to loan at an interest rate of 10% per year is $2,678,795.44.