$21.$ Imagine you have won the lump sum amount of $$1400$ in a recent contest. However, you must wait until the end of $5$ 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 $5$ years.

Using an interest rate of $3\mathrm{.}50\%,$ determine the unknown lump sum amount that would make the present value of both prizes equivalent.

$$1103\mathrm{.}08$

$$928\mathrm{.}76$

$$1178\mathrm{.}76$

$$1365\mathrm{.}84$

$$210\mathrm{.}49$