Q$5.$ a$)$ Mr$.$ Phaneesh, Finance Manager of M$/$S Ruby Industries Ltd$,$ needs Rs$.20,00,000$ for the expansion

of Ere of his plants. One of the vendors offers him the following proposal: make a down payment of $20\%$

and borrow the remaining amount from their banker @ $8\%$ interest rate p$.$a$.$ The terms of the bank are such

that the loan has to be repaid in $8$ equal annual installments starting four years from now. If Mr$.$ Phaneesh

accepts this proposal, what is the amount of annual installment that he has to pay to the bank?

b$)$ Mr$.$ Ram received Rs$\mathrm{.}50,000$ as a gift from his grandfather. He immediately placed Rs$\mathrm{.}10,000$ in a mutual

fund earning $12\%$ per annum, compounded quarterly. He plans to use the remaining Rs$.40,000$ to start a

new business. After $2$ years he has Rs$.1,00,000$ in his business. He again takes Rs$.20,000$ of Rs$.1,00,000$

and places it in the same mutual fund earning the same return. After $10$ years from the second investment,

he lost all his money in the business. However, that day he receives a statement from the mutual fund. How

much are his deposits now worth?