Question

find the number of years required to reach the intended future value at the given rate: p=$2250, FV=$5000, r=6.2%

Answer 1

Simple Interest

Given a situation where an investment of P dollars is made at a rate r for t years, the interest earned is given by:

I = P.r.t

The final value (FV) is the sum of the principal p and the interest earned:

FV = P + P.r.t

Factoring P:

FV = P (1 + r.t)

This equation allows calculating the final value when we know P, r, and t. If we need to know the value of t, we solve the previous equation for t:

FV = P (1 + r.t)

Dividing by P:

1 + r.t = FV/P

Subtracting 1:

r.t = FV/P - 1

Dividing by r:

$t=\frac{\frac{FV}{P}-1}{r}$

The data provided in the question is p=$2250, FV=$5000, r=6.2%.

Converting to decimal: r=0.062. Substituting:

$t=\frac{\frac{5000}{2250}-1}{0.062}=\frac{1.22222}{0.062}=19.71$

The time required is approximately 20 years (rounding up)