Compare simple and compound interest

Noah is comparing two ways of calculating interest for a short-term savings account

Both plans start with $10,000 at 10% p.a. The term is 4 years

Plan A uses compound interest, compounded annually. Plan B uses simple interest

The compound plan has one compounding period per year

These fictional plans have fixed rates, no fees and no deposits, withdrawals or repayments during the term. Any debt is repaid at the end. For the compound plan the quoted annual rate is nominal. Keep full calculator precision until the final answer

In the formulas, R is the annual percentage number, r = R/k is the percentage number per compounding period, k is periods per year and n = kt