Question

The simple interest on a certain sum of money for 4 years at 15 percent per annum is 600. Find the compound interest in the same sum at 10 percent interest for 2 years *

Answer 1

Answer:

210

Step-by-step explanation:

The amount, $A$, after applying a simple interest, $i$, on a principal, $P$, for a period of $t$ years is given by

$A=P*(1+\frac{i}{100}*t)$

In our case;

P is unknown

t=4

i=15%

I=600

Also, the amount can be expresses as

$A=P+I$

Therefore

$P+600=P*(1+\frac{15}{100}*4)\\ P+600=P(1+0.15*4)\\P+600=P*1.6\\1.6P-P=600\\0.6P=600\\P=1000$

Therefore the principal amount is 1000

Now we can compound this principal using the formula

$A=P*(1+\frac{i}{100})^t$

Here

P=1000

i=10%

t=2 years

Therefore the amount is given as

$A=1000*(1+\frac{10}{100} )^2\\A=1000*1.1^2\\A=1210$

The compound interest earned in the two years is;

$1210-1000=210$