1. You played the 6/49 Lottery with winning numbers of {10, 12, 18, 22, 26, 28} and won PhP 20M. Assume you invested half of it in a bank yielding 8% interest compounded annually, while you used the other half to celebrate and bought a luxury car that depreciates in value by 5% annually. Compound interest is when you earn interest on both the money you invested and the interest you earned. Depreciation, on the other hand, is the reduction of value of an asset (e.g. luxury car) over time due to use, wear and tear. The depreciation value is computed based on the remaining value of the asset.

A. (4 pts) What is the recurrence relation that represents the amount in the bank at the end of the nth year? Write the expression in its simplest form.

B. (4 pts) What is the recurrence relation that represents the value of the car at the end of the nth year? Write the expression in its simplest form.

C. (4 pts) How much money do you have at the end of the 10th year, assuming you sold the car at the end of the 10th year? No need to compute for the final value. Just write the expression in its simplest form.