Sub: managerial mathematics please answer them and show all the necessary steps. formula table is given below. will give thumbs up

d) If $300,000 is to be saved over 25 years, how much should be deposited quarterly if the investment earns 8% interest compounded quarterly? FORMULAE 1. Linear Equations (1) Slope of a line, m= Y: - X-X, Point-slope form, y-y = m(x - x) (111) Slope-intercept form, y = mx +b (where m = slope, b = y-intercept) (iv) General form, Ax+By+C =0 2. Mathematics of Finance a) Simple Interest (1) Interest, I = Prt Accumulated amount. A = P (1 + rt) Where P = principal, r = interest rate, t = number of years b) Compound Interest (1) Accumulated amount, A=P(1+i)" Present value for compound interest, P = 4(1+i)** Where i = ", n = mt, and m = number of conversion periods per year m c) Effective Rate of Interest -1 1+ m d) Annuities Notations i= m r and n=mt (11) Future value of an annuity (1+i)"-1 S=R (4=;*' Present value of an annuity 1-(1+i)" PER Where S = future value of ordinary annuity of n payments of R dollars periodic payment Where P = present value of ordinary annuity of n payments of R dollars periodic payment e) Sinking Fund and Amortization Notations: 1 =- and n = mt m (11) Sinking Fund formula Si R- (1+i)" -1 Amortization formula Pi R= 1-(1+i)" Where R= periodic payment required to accumulate S dollars over n periods Where R = periodic payment on a loan of P dollars to be amortized over n periods 3. Rules of Differentiation a) Derivative of a constant: If f(x)is a constant, then f'(x)=0 b) Power rule : If f(x) is x, then f'(x)= nx-1 c) Constant multiple rule: Derive cf(x)= cf'(x) (c is a constant) d) Sum rule: Derive f(x)+ g(x) = f'(x)+ g'(x) du u V e) Product rule: If f(x)=uxv, then f'(x)=u +y dx dx du dy -U f) Quotient rule: If f(x)= then f'(x)= dx dx [v] g) Chain rule: Derive g[f(x)]=g'[f(x)]f'(x) h) General power rule: Derive [f(x)}" =n[f(x)]*4 f'(x) 1) Exponential function: Derive et = e* Derive (e)=e" [u'(x)] 1 j) Logarithmic function: Derive Inx== Derive (nu(x)=(eta) (2[3] ][+(+)]