Need full working out, help please

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

$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%

12.5% annual interest rate