Could someone please check my work?

what amount would you need to invest in a savings account or The beginning of each of The following 48 months To end up with a balance of $250, 000 or The end of those 4 years if you know That The account earns a nominal interest rate of 5% compounded monthly? Ler n = 48 = number of Times account accrues 1/48 th of its nominal interest, and let P. denote The starting balance / principle . P ( 1 + - ) " = 250, 000 note : ( 1 + 4 8 )= 1. 00104 1667 = P( 1 + 48 ) = 250,000 = 100. 1041667% -> P =. 250,000 = $237, 813. 5448 (1 + :05) 48 Hence, you'd need to invest (1+:05 ) ~100.1%% of The previous month's balance after initially investing $ 237, 813. 54 into savings TO end up with $250, 000 or The end of The 4-year Term