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:
[tex]I=Prt[/tex]
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:
[tex]\displaystyle r=\frac{I}{P.t}[/tex]
Substituting:
[tex]\displaystyle r=\frac{450,000}{350,000\cdot 19}[/tex]
Calculating:
r = 0.0677
Or, equivalently:
r = 6.77%
The annual interest is 6.77%
The annual interest rate that should be earned for reaching the goal should be 6.77%.
Since the parents will get retired in 19 years. They presently have a saving amount of $350,000, and they think they require $800,000 at the time of retirement.
So here the rate of interest should be
= (Requirement - saving amount) / (Saving amount * number of years)
= $450,000 / (350,000 .19)
= 6.77%
hence, The annual interest rate should be 6.77%.
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