4.the amount in an account which was opened 180 days ago is RM205. iF the account was offered a simple interest of 5 percent per annum, find the original principal.

#4. in half a year, it grew by half of 5%, so it started out as

205.00/1.025 = 200.00

#5. Ummm, four years?

#5.how long does it take a sum of money to double itself at a simple interest rate of 6 percent annum ?

well, what's 1/.06 ?

no, 1/.06 is not 6%

1/.06 = 16.66 is the number of years it takes to double the money.

every year adds 6% after 16.66 years, 100% has been added. The money has doubled.

To find the original principal in question 4, you need to use the formula for simple interest:

Simple Interest = (Principal * Interest Rate * Time) / 100

Given:
Amount(A) = RM205
Interest Rate(I) = 5%
Time(T) = 180 days

First, convert the time from days to years:
Time(T) = 180 days / 365 days/year = 0.4932 years (approximately)

Now, substitute the given values into the simple interest formula:
205 = (Principal * 5 * 0.4932) / 100

To solve for the Principal, rearrange the formula:
Principal = (205 * 100) / (5 * 0.4932)

Using a calculator, evaluate the expression:
Principal = 4160.4648

Therefore, the original principal in the account is approximately RM4160.

For question 5, to find the time required for a sum of money to double itself, you need to use the formula for compound interest.

The formula for compound interest is:

Amount(A) = Principal(P) * (1 + (Interest Rate(I) / 100)) ^ Time(T)

Given:
Principal(P) = 1 (as the initial sum of money)
Interest Rate(I) = unknown
Time(T) = 4 years

We want the amount to double, so the final amount(A) will be 2 times the principal(P).

Substituting the values into the compound interest formula:
2 = 1 * (1 + (I / 100)) ^ 4

Rearranging the formula to solve for the Interest Rate(I):
(I / 100) = (2 ^ (1/4)) - 1

Multiply both sides by 100 and simplify:
I = (2 ^ (1/4) - 1) * 100

Using a calculator, evaluate the expression:
I = (1.189207115 - 1) * 100

I ≈ 18.92

Therefore, it will take approximately 18.92% interest rate to double the sum of money in 4 years.