Precalcus 12 fiancé and investing

Question

Determine which of the following investments will have a greater rate of return.

A. A five year $40000 GIC that earns an annual rate of interest of 6.5% compounded annually.

B. A five year $10000 CSB that pays simple interest of 7.8% per year.

C. An investment where $2500 is deposited each month into an account for five years that pays annually rate of interest of 9.8% compounded semi-annually.

Answer 1

A 40K at 6.5% compounded annually

A = P(1+r/n)^nt = 40,000(1+.065)^5) = 40,000(1.065)^5= $54,803.47 in 5 years

r= rate of annual interest, n= number of periods per year. t= number of years, P= original investment

6.5% in first year adds $2600. then 6.5% of $42,600 totals $45,369 at end of year 2

1.065 x 45369 = 48,317.985 at end of year 3

1.065 x 48,317.985 = 51,458.65403 after 4 years

1.065 x 51,458.65403 = $54,803.47 after 5 years

$40K earned $15,803.47 interest over 5 years

15,803.47/5 = about average 7.4 % annual return > 6.5% due to compounding

B 10K at 7.8% simple interest, no compounding, annually

A = Pt(1+r) =10,000(5)(1.078) = $53,900 in 5 years

That's an interest return of 43,900 which is 43,000/10,000 = 4.3 = 430% rate of return

over 5 years. 430/5 = 86% average rate of return per year

C 2,500 monthly at 9.8% annual interest rate, compounded semi-annually, for 5 years

PV = P[1-(1+r)^-n]/r where P = 2,500, n = number of periods, r = rarte of interest per period

= 2,500[1-(1+ )^ ]/r

B has a greater rate of return than A

C has a rate of return = probably worse than A or B

an annuity calculator online can do the arithmetic with least or no effort

C earns interest per year on an average about maybe 6.8%

per dollar invested, B has the best rare of return