To determine the monthly payment, we will use the formula for the present value of an ordinary annuity:
PV = PMT * (1 - (1 + r/n)^(-nt)) / (r/n),
where:
PV = Present value (the amount of the loan or investment)
PMT = Monthly payment
r = Interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
Given:
PMT = $166.57
r = 8% = 0.08
n = 12 (since it's compounded monthly)
t = 6
Plugging in the values, we have:
PV = 166.57 * (1 - (1 + 0.08/12)^(-12*6)) / (0.08/12).
PV = 166.57 * (1 - (1.00666666666667)^(-72)) / (0.00666666666667).
PV = 166.57 * (1 - 0.541751104042) / 0.00666666666667.
PV = 166.57 * 0.458248895958 / 0.00666666666667.
PV = 12089.44108849 / 0.00666666666667.
PV ≈ 1,813,444.14 (approximately).
Therefore, the present value of the loan is approximately $1,813,444.14.
Monthly payment of $166.57 with a fixed compound interest rate of 8% compounded monthly; payments made monthly over a period of 6 years
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