Two loans for equal amounts are repaid at an effective interest rate of $4\%.$ Loan $1$ is to be

repaid with $20$ equal annual payments. Loan $2$ is to be repaid by $20$ annual payments, each

containing equal principal amounts $($equal principal repayment$)$ plus an interest amount

based on the unpaid balance.

Payments are made at the end of each vear.

The annual payment for Loan $1$ first ex$-$

ceeds the annual payment for Loan $2$ with the nth payment.

Find n$.$

Find n$.($Hint: Let L is the loan amount.

Then the first payment of the Loan $2$ is

consisted of the sums of the interest amount L $*\mathrm{.}04$ and the principal repaid amount

L$/20.)$