Question

PLS HELP! 70 POINTS!!

Mr. Mudd gives each of his children $2000 to invest as part of a friendly family competition. The competition will last 10 years. The rules of the competition are simple. Each child can split up his or her $2000 into as many separate investments as they please. The children are encouraged to do their research on types of investments. The initial investments made may not be changed at any point during the 10 years; no money may be added and no money may be moved. Whichever child has made the most money after 10 years will be awarded an additional $10,000.
The table shows the investment made by each of Mr. Mudd’s children, and what happened to their investment over the decade long friendly competition.
Child Performance of investments over the course of the competition
Albert $1000 earned 1.3% annual interest compounded monthly
$500 lost 3% over the course of the 10 years
$500 grew compounded continuously at rate of 0.7% annually
Marie $1500 earned 1.3% annual interest compounded quarterly
$500 gained 3% over the course of 10 years
Hans $2000 grew compounded continuously at rate of 0.8% annually
Max $1000 decreased in value exponentially at a rate of 0.6% annually
$1000 earned 1.9% annual interest compounded biannually (twice a year)
Make sure to show your work
1. What is the balance of Albert’s $2000 after 10 years?
2. What is the balance of Marie’s $2000 after 10 years?
3. What is the balance of Hans’ $2000 after 10 years?
4. What is the balance of Max’s $2000 after 10 years?
5. Who is $10,000 richer at the end of the competition?

Answer 1

Albert = $2159.07; Marie = $2244.99; Hans = $2188.35; Max = $2147.40

Marie is $10 000 richer

Explanation:

Albert

(a) $1000 at 1.2 % compounded monthly

A = P (1 + r/n )^nt

A = 1000(1 + 0.001)¹²⁰ = $1127.43

(b) $500 losing 2%

0.98 × 500 = $490

(c) $500 compounded continuously at 0.8%

A = Pe^rt

= 500e^0.008 * 10

= $541.64

(d) Balance

Total = 1127.43 + 490.00+ 541.64 = $2159.07

Marie

(a) 1500 at 1.4 % compounded quarterly

A = 1500(1 + 0.0035)⁴⁰ = $1724.99

(b) $500 gaining 4 %

1.04 × 500 = $520.00

(c) Balance

Total = 1724.99 + 520.00 = $2244.99

Hans

$2000 compounded continuously at 0.9 %

A = 2000e^0.009 * 10

= $ 2188.35

Max

(a) $1000 decreasing exponentially at 0.5 % annually

A = 1000(1 - 0.005)¹⁰= $951.11

(b) $1000 at 1.8 % compounded biannually

A = 1000(1 + 0.009)²⁰ = $1196.29

(c) Balance

Total = 951.11 + 1196.29 = $2147.40

Marie is $10,000 richer at the end of the competition.

Hope this helps!!! :)