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

Answer:

p = $3,478.26

Step-by-step 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:

$A=p(1+r\,t)\\\frac{A}{(1+r\,t)} = p\\p=\frac{A}{(1+r\,t)}$

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:

$p=\frac{A}{(1+r\,t)}\\p=\frac{14,000}{1+0.055\,*\, 55} \\p=\frac{14,000}{1+3.025} \\p=\frac{14,000}{4.025} \\p=3478.26$

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