Consider Rs. P as the monthly installment

Period (x)

\[=\text{ }1\text{ }year\]

\[=\text{ }12\text{ }months\]

Since,

Total principal for one month

\[=\text{ }P\text{ }\times \text{ }\left[ x\text{ }\left( x\text{ }+\text{ }1 \right) \right]/\text{ }2\]

Putting the value of x

\[=\text{ }P\text{ }\times \text{ }\left( 12\text{ }\times \text{ }13 \right)/\text{ }2\]

Or,

\[=\text{ }78P\]

Interest

\[~=\text{ }PRT/\text{ }100\]

Putting the values

\[=\text{ }\left( 78P\text{ }\times \text{ }14\text{ }\times \text{ }1 \right)/\text{ }\left( 100\text{ }\times \text{ }12 \right)\]

Now, we have

\[=\text{ }0.91P\]

So the amount of maturity

\[=\text{ }P\text{ }\times \text{ }x\text{ }+\text{ }SI\]

\[6455\text{ }=\text{ }P\text{ }\times \text{ }12\text{ }+\text{ }0.91P\]

\[6455\text{ }=\text{ }12.91P\]

Or,

\[P\text{ }=\text{ }6455/12.91\]

\[=\text{ }Rs.\text{ }500\]