Answer: The present value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:
PV = PMT * [ (1 - (1 + r)^-n) / r ] * (1 + r)
where:
PMT = $300 (the monthly payment)
r = 0.06/12 (the monthly interest rate)
n = 10*12 (the number of periods over 10 years, with 12 months in a year)
Plugging in the values into the formula, we get:
PV = $300 * [ (1 - (1 + 0.06/12)^-n) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * [ (1 - (1 + 0.06/12)^-(10*12)) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * [ (1 - 1.06^-120) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * [ (1 - 0.379362539) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * [ (0.620637561) / (0.06/12) ] * (1 + 0.06/12)
PV = $300 * 10.34300138
PV = $31,029.
So the present value of the annuity due is $31,029. This means that if you were to invest $31,029 today, you would receive a monthly payment of $300 for 10 years at 6% interest compounded monthly.
Explanation: