$1000 was invested for two years at 10% simple interest .calculate the effective rate was earned.
pls check my solve
(1+0.1/2)^2-1
= 0.1025
but the true answer is 9.54%
pls help me to get the formula of effective rate
Interest earned was simple interest, so in two years, the future value is
1000(1+2*0.1)=1200
With compound interest of rate i, the equivalent interest would be
1000(1+i)²=1200
or
(1+i)=√(1200/1000)=1.095445
or 9.54% approx.
To calculate the effective rate earned, you can use the formula for compound interest:
Effective Rate = (1 + (Interest Rate / Number of Compounding periods))^(Number of Compounding periods) - 1
In this case, the interest rate is 10% and the investment is for two years. However, since simple interest is being used and not compound interest, we need to convert the 10% simple interest to an equivalent compound interest rate.
To do this, we need to determine the equivalent compound interest rate with the same final amount after two years. We can use the formula for simple interest:
Final Amount = Principal + (Principal * Interest Rate * Time)
Since we know the final amount after two years is $1000 and the principal amount is also $1000, we can rearrange the formula to find the equivalent compound interest rate:
Interest Rate = (Final Amount - Principal) / (Principal * Time)
= ($1000 - $1000) / ($1000 * 2)
= 0 / $2000
= 0
Since the interest rate in this case is 0%, the effective rate earned will also be 0%.
Therefore, the true answer is indeed 0%, not 9.54%.