The present value P that will amount to A dollars in n years with interest compounded annually at annual interest rate r, is given by P = A (1 + r) -^n. Find the present value that will amount to $50,000 in 20 years at 8% compounded annually.

Question

The present value P that will amount to A dollars in n years with interest compounded annually at annual interest rate r, is given by P = A (1 + r) -^n. Find the present value that will amount to $50,000 in 20 years at 8% compounded annually.

Answer 1

P = 50000(1.08)^-20

= ......

On your calculator
enter 50000 x 1.08 Y^X 20 ± =
to get 10,727.41

Answer 2

To find the present value, P, that will amount to A dollars in n years with interest compounded annually at an annual interest rate r, you can use the formula:

P = A / (1 + r)^n

In this case, A is $50,000, n is 20 years, and r is 8% or 0.08.

Now we can substitute the values into the formula and calculate the present value:

P = 50000 / (1 + 0.08)^20

To simplify the calculation, first, add 1 to the interest rate and raise it to the power of n:

(1 + 0.08)^20 = 1.08^20

Now we can substitute this value back into the formula:

P = 50000 / 1.08^20

Using a calculator, raise 1.08 to the power of 20, and then divide 50,000 by that result to get the present value:

P ≈ 50000 / 4.661616352 = $10,712.99

Therefore, the present value that will amount to $50,000 in 20 years at 8% compounded annually is approximately $10,712.99.

The present value P that will amount to A dollars in n years with interest compounded annually at annual interest rate r, is given by P = A (1 + r) -^n. Find the present value that will amount to $50,000 in 20 years at 8% compounded annually.

P = 50000(1.08)^-20

122222

To find the present value, P, that will amount to A dollars in n years with interest compounded annually at an annual interest rate r, you can use the formula: