The Simple Interest accurued on an amount.

Question

The Simple Interest accurued on an amount of 24000 at the end of 2 years is 11,520. Find the C I accrued on the same amount at the same rate of interest, for the same period? Ans: C I = 12,902.40

My Try: A = 24,000

T = 2 Years

S I = 11,520

P R T /100 = 11,520

A = S I + P

24,000 = P + 11,520

P = 12,480

Now putting P value in S I Formulae to get rate of interest.

11,520 = (12,480 * 2 * R )/100

11,520*5/1248 = R

R = 46 %

Now putting R value in C I on same amount.

= 24,000 {([1 + 46/100]^2) -1}

= 24,000 {([1.46]^2)-1}

= 27,158 (Does n’t match final answer why?, not even close to it)

Answer 1

I'm not familiar with all the financial formulae, but the concepts are simple. Simple interest is always calculated on the original principal.

Interest per year is $\frac{$11520}{2} = \$5760$, giving an annual interest rate of $\frac{5760}{24000} \times 100\% = 24 \%$.

Assuming that's compounded annually, in two years you would have $1.24^2$ of your original investment.

The proportional increase would be $1.24^2 - 1 = 0.5376$.

In absolute terms, that's a compound interest of $0.5376 \times \$24000 = \$12902.40$.

Answer 2

For simple interest,

$A(2)=(24000+11520)=24000(1+2i)$

We get $i=0.24$

For compound interest,

$A(2)=24000(1+0.24)^2=36902.4$

$I_{[2,0]}=A(2)-A(0)=36902.4-24000=12902.40$