Question

Sam and Brian plan to send their son to university. To pay for this they will contribute equal monthly payments to an account bearing interest at an annual rate of 4.8%, compounded monthly. They will make these payments for 10 years. Five years after their last contribution, they will begin the first of 60 monthly withdrawals of $2,960 to pay the university's installment bills. How large must their monthly contributions be? Answer = $ 554.81 X (Round to the nearest cent/penny.)

Answer 1

let p amount will contribute by both Sama and Brian. and rate = 4.8. = 4.8 Too r = 0.048 Amount ofter 1st month A = P(1+r) +P After Ilhd month A2=(PC++v)'+P )(1+y)+ +P = P(1+ry2 + PC1+r) + P After I'd month A3=(P(1 + 2 + P(+8) +P)(1+x)=P Az = P(177)3+ P(1+ry2 + P(1+r) + P After 60 months=) Abo= P(1+0)89 Plitry S8 Plhos?+--+P AGO 111+V)60 P Itr- Abo= 326.25P (1+r)-1 Amonnt at the end of 60th month is Ä. Then Da 326.25P let A = let Pi is the amount ofter Ist installment - Pi = A(1+y)'-m where 'm'= amout of installment.

Amount after Ind installment P2=(Ali+r)-m) (1+r)-m Amount after P3 = A[i+r93 - m (i+ry2-meitra-m after hard installment - After both installment amount should be zero. Allting 60mm 1(1+r)59 Ir-1 ! ) A Ali+ry 60 (1.048959 0.048 M (1.048)54-1 |(1.048)60X0.098 (310.08 m ) 10.048)60 Now put whlul of À and 'm' 326.25 p = 2960x18.62. А P= 164.01$ Hence total amount contributed by both will be $ 169