Imagine you have won the lump sum amount of $$1050$ in a recent contest. However, you must wait until the end of $7$ years to receive the money.

However, you would prefer a different pattern of payments: $$225$ today and then receive some unknown LUMP SUM $($i$.$e$.$ one time$)$ amount that will be received in $7$ years.

Using an interest rate of $6\mathrm{.}50\%,$ determine the unknown lump sum amount that would make the present value of both prizes equivalent.

$$700\mathrm{.}35$

$$144\mathrm{.}79$

$$1282\mathrm{.}04$

$$675\mathrm{.}68$

$$450\mathrm{.}68$