Question

Determine the present value P you must invest to have the future value A at simple interest rate r after time t.

A​ = ​$14 comma 00014,000​, r​ = 5.55.5​%, t​ = 55 years
Equation : A=p(1+rt)

Answer 1

p = $3,478.26

Explanation:

Since they give you the formula for the future value at simple interest rate, and we need to find the present value p, we can solve for the variable p in the formula, isolating it on one side of the equal sign, and then replacing the known values to find the numerical answer:

1) Solve for p first in the formula:

`A=p(1+r\,t)\\(A)/((1+r\,t)) = p\\p=(A)/((1+r\,t))`

2) we replace A with the given $14,000, t with 55 years, and r with the decimal form of the 5.5 percent rate, that is: 0.055:

`p=(A)/((1+r\,t))\\p=(14,000)/(1+0.055\,*\, 55) \\p=(14,000)/(1+3.025) \\p=(14,000)/(4.025) \\p=3478.26`

Therefore,the present value to be invested is: $3,478.26