Question

Sujatha borrows Rs. $12,500$ at $12$% per annum for $3$ years at simple interest and Radhika borrows the same amount for the same period at $10$% per annum compounded annually. Who pays more interest and by how much?

Answer 1

Simple Interest

$SI=$Rs$\frac{12500\times 12\times 3}{100}=$Rs$4500$

Compound Interest

Interest for the $1$st year$=Rs\frac{12500\times 10\times 1}{100}$

$=Rs1250$

Amount After the $1$st year$=Rs12500+$Rs$1250$

$=13750$

Interest for the $2$nd year$=\frac{13750\times 10\times 1}{100}$

$=1375$

Amount After the $2$nd year$=13750+$Rs$1375$

$=15125$

Interest for the $3$rd year$=\frac{15125\times 10\times 1}{100}$

$=1512.50$

Amount After the $3$rd years$=15125+1512.50$

$=16637.50$

Compound Interest$=16637.50-$Rs $12500$

$=4137.50$

Sujata pays more interest than Radhika by Rs$(4500-4137.50)=$Rs$362.50$