When Roberta borrowed $$$$1157\mathrm{.}00,$ she agreed to repay the loan in two equal$$ payments, to be made $20$ days and $100$ days from the day the money was borrowed. If interest is $7\%$ on the$$ loan, what is the size of the equal payments if a focal date of today is$$ used?

Represent the payments made at each of the times with variable expressions. Then use the present value formula to find the equivalent values of those payments today. Use these two variable expressions and the known loan amount to solve for the amount of the equal payments. The present value formula is shown$$ below, where P is the present$$ value, S is the future$$ value, r is the rate of interest$($expressed as a$$ decimal$),$ and t is the time in years.

Upper PequalsStartFraction Upper S Over $1$ plus rt EndFraction