Question

What is the principal, if a person paid an amount of $432 after 1 year at 8% rate of interest per annum

Answer 1

To determine the principal amount that resulted in a total payment of $432 after one year at an 8% rate, we rearrange the simple interest formula. The calculation reveals that the principal was $400.

Step-by-step explanation:

The question asks to find the principal amount that, when invested at an 8% annual interest rate, results in a total amount of $432 after 1 year. To find the principal, we use the formula for simple interest, which is:

Interest = Principal × rate × time

Since we are given the final amount, which includes the principal and the interest, we can also write this as:

Total Amount = Principal + Interest

And since Interest = Principal × rate × time, we can substitute the interest part with the product of principal, rate, and time:

Total Amount = Principal + (Principal × rate × time)

Rearranging the formula to solve for the principal gives us:

Principal = Total Amount / (1 + rate × time)

By inserting the given values:

Principal = $432 / (1 + 0.08 × 1)

Principal = $432 / 1.08

Principal = $400

Therefore, the initial principal amount was $400.

Answer 2

principal = $400

Step-by-step explanation:

amount(a)=principal(p) + interest(y).........(1)

Interest(y)=principal(p) x rate(r) x time(t)....(2)

In (1), p= a - y...........(3)

putting (3) in (2),

y = (a - y) x r% x t

y = (432 - y) x 8% x 1

y = 3456%-8y%

y + 0.08y = 3456%

1.08y = 34.56

y = 32

but a - y = p

432 - 32 = p

p = 400

principal = $400