I had a 10 question practice worksheet before a test, and I am completely stumped on these last two questions. Please help?

Question

1) Jennifer wants to invest some money now to buy a new tractor in the future. If she wants to have 350,000

available in 4 ​years, how much does she need to invest now in a CD paying 4.25​% interest compounded monthly?

2) You are given a choice of taking the simple interest on 100,000 invested for 4

years at a rate of 5​% or the interest on 100,000 invested for 4 years at an interest rate of 5​%

compounded quarterly. Which investment earns the greater amount of​ interest? Give the difference between the amounts of interest earned by the two investments.

Answer 1

Let M = money at the end of the period

I = the annual interest rate

M_o = money invested at the beginning of the period

n = the number of periods

t = time in years

1) M = M_o(1 + I/n)^nt $350,000 = M_o(1 + .0425/12)^(12*4) = M_o(1.18495)

or M_o = $295,371.40

2) You know that the money invested quarterly will always earn more that the simple interest by general rule!

In the first case, M = 100,000(1 + .05)⁴ = 121,550.63 So, the interest earned is $21,550.63

In the second case, M = 100,000(1 + .05/4)^(4*4) = 121,988.95 So, interest earned is $21,988.95

Therefore, she earns $21,988.95 - $21,550.63 = $438.32 more with quarterly compounding!