You plan build a sunroom on to your house in 6 months. You will pay for the sunroom in 3 installments of $10,000 each. The first payment is seven months from now and the other two payments are eight and nine months from now. If your investments earn 5% APR, compounded monthly, how much must you invest today to cover the cost of the sunroom?
Amount payable (p)= 10000
First payment due month (n)= 7
Second Payment due month (n)= 8
Third Payment due month= 9
investment rate = 5% compounded monthly
monthly rate (i)= 0.05/12= 0.004166666667
Today invested Amount = sum of Present value of all
amounts
present value formula = P/(1+i)^n
10000/(1+0.00416666667)^7+ 10000/(1+0.00416666667)^8+
10000/(1+0.00416666667)^9
=$29018.65977
So, amount invested today is 29018.66
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