Homework Answers

Three years ago Lilly borrowed R10 000 from Faith on condition that she should pay her back two years from now. She also owes Faith R6 000 payable five years from now. The applicable interest rate for both transactions is 13,75% per year, compounded every six months. After considering her payback schedule, Lilly asks Faith if she can pay her R9 000 now and the rest in four years' time. She agrees on condition that the new agreement will run from now and that an interest rate of 16,28% per year, compounded monthly, will be applicable from now. The amount that Lilly will have to pay Faith four years from now is

A loan will be paid back by means of payments of R250 each, every six month for ten years. An interest rate of 5% per year, compounded every six months, will be applicable. The present value of the loan is

A nominal interest rate of 19,40% per year, compounded monthly, is equivalent to a continuous compounding rate of

If R35 000 accumulates to R48 320 at a continuous compounded rate of 8,6% per year, then the term under consideration is

Mapuleng deposits R1 500 at the end of every month into an account that earns 12,5% interest per year, compounded monthly. After two years, she stops making these monthly contributions because the interest rate changes to 15% per year, compounded every two months. If no withdrawals or deposits are made for four years the balance in the account will be

Sbusiso needs R150 000 on 17 November 2022 to upgrade his restaurant. On 8 January 2022 he deposited an amount into an account earning 13,45% interest per year, compounded monthly, and being credited on the 1st of every month. If fractional compounding is used for the full term, then the amount that Sbusiso deposited on 8 January 2022 was

Kagiso wants to buy a new gaming computer for R40 000. He decides to save by depositing an amount of R400 quarterly into an account earning 16% interest per year, compounded quarterly. The approximate number of quarters it will take Kagiso to have R40 000 available is

1. For what values of h the vectors

⟶ [ 1 ⟶ [ -1 ⟶ [ 5

u = -3 u_{2 =} 9 u₃ = -7 <--- u₁, u₂, and u₃ are vectors

-2] -6] h]

are linearly independent?

1.Consider the plane ℿ₁ : 3z + 2y + x = 2.

a.) If ℿ_{2 :} 2z - 3y = 1 is another plane. Are the planes ℿ₁ and ℿ₂ orthogonal?

b.) Consider the line L that passes through the point P₀(0, 1, 1) and is parallel to the vector

⟶

u = [ 1

1 Find the point of intersection of the plane ℿ₁ and the line L.

1]