An annuity with semiannual payments has an initial payment of $1.$ Each subsequent payment is $1$ more than its preceding payment until reaching a payment of $25.$ Following the payment of $25,$ the next seven payments are each equal to $26.$ Following the last payment of $26,$ payments decrease by $1$ each semiannual period until reaching a final payment of $1.$ Determine the accumulated value of the annuity immediately after the last payment, usin an annual effective interest rate of $10\%.$ a$)3520,$ b$)3580,$ c$)3640,$ d$)3700,$ e$)3760$