Answer:
First problem: $410000
Second problem: 12.5%
Step-by-step explanation:
First problem:
Use the simple interest formula,
I = Prt
where
I = interest earned
P = principal amount (initial amount)
r = annual interest rate written as a decimal
t = time written as number of years
Here you have
t = 6 years
r = 5% = 0.05
I = $123000
I = Prt
123000 = P * 0.05 * 6
0.3P = 123000
P = 410000
Answer: $410000
Second problem:
The problem involves the principal and simple interest. We can derive a formula for future value of a simple interest investment or loan.
We have the simple interest formula from above.
I = Prt
Now we add the principal to find the future value:
A = P + Prt
A = P(1 + rt)
where
A = future value (after adding the interest)
P = present value (before adding the interest)
r = annual interest rate written as a decimal
t = number of years
P = $2800
t = 120 days = (120 days)/(360 days/year) = 1/3 year
A = $2917
A = P(1 + rt)
2917 = 2800(1 + r * 1/3)
2917 = 2800 + 2800r/3
2800r/3 = 117
2800r = 351
r = 0.125 = 12.5%
Answer: 12.5% annual interest rate
