Imagine you have won the lump sum amount of $$1400$ in a recent contest. However, you must wait until the end of $3$ years to receive the money.

However, you would prefer a different pattern of payments: $$250$ today and then receive some unknown LUMP SUM $($i$.$e$.$ one time$)$ amount that will be received in $3$ years.

Using an interest rate of $5\mathrm{.}50\%,$ determine the unknown lump sum amount that would make the present value of both prizes equivalent.

$$942\mathrm{.}26$

$$1350\mathrm{.}38$

$$212\mathrm{.}90$

$$1106\mathrm{.}44$

$$1192\mathrm{.}26$