#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 in four years ?
205.00/1.025 = 200.00
#5. Ummm, four years?
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.
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.