Question

Your parents will retire in 19 years. They currently have $350,000 saved, and they think they will need $800,000 at retirement. What
annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds?

Answer 1

Answer:

The annual interest is 6.77%

Step-by-step explanation:

Simple Interest

Definition: Interest calculated on the original principal only of a loan or on the balance of an account.

Unlike compound interest where the interest earned in the compounding periods is added to form the new principal, simple interest only considers the principal to calculate the interest in every period.

The interest earned is calculated as follows:

$I=Prt$

Where:

I = Interest

P = initial principal balance

r = interest rate

t = time

Your parents will retire in t = 19 years. They have P=$350,000 in their savings account and they need to have $800,000 when they retire.

The interest earned is the difference between the final balance and the principal:

I = $800,000 - $350,000 = $450.000

Solving the first equation for r:

$\displaystyle r=\frac{I}{P.t}$

Substituting:

$\displaystyle r=\frac{450,000}{350,000\cdot 19}$

Calculating:

r = 0.0677

Or, equivalently:

r = 6.77%

The annual interest is 6.77%