High School

A perpetuity pays 1800 dollars on January 1 of 1980, 1982, 1984, and pays X dollars on January 1 of 1981, 1983, 1985, and so on. If the present value on January 1, 1975, is 29000 dollars, and the effective rate of interest is 6.9 percent, what is X?

Answer :

Final answer:

To find X, we use the present value formula. The present value of X is $24623.05.

Explanation:

To find the value of X, we need to calculate the present value of the perpetuity. Since the effective rate of interest is 6.9 percent, we can use the formula: Present value = Cash flow / Interest rate.

For the cash flows on January 1 of 1980, 1982, and 1984, the present values are: $1800 / (1 + 0.069)^5 + $1800 / (1 + 0.069)^3 + $1800 / (1 + 0.069) = $1371.81 + $1460.30 + $1544.84 = $4376.95.

Subtracting this from the total present value of $29000, we get the present value of X as: $29000 - $4376.95 = $24623.05.

Therefore, X is equal to $24623.05.

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