Math question

Question

A $2000 investment with interest compounded semi-annually is worth $2600 after 5 years. What is the yearly rate for this investment 

Answer 1

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

 

A = future amount = 2600

P = principal investment = 2000

r = interest rate as decimal = to be determined

n = # times compounded per year = 2

t = time in years = 5

 

2600 = 2000(1+r/2)²⁽⁵⁾

2600 = 2000(1+r/2)¹⁰

 

(1+ r/2)¹⁰ = 2600/2000

(1+r/2)¹⁰ = 1.3

 

Take the 10th root of each side

 

1 + r/2 = ¹⁰√1.3

 

r/2 = ¹⁰√1.3 -1

 

r = 2(¹⁰√1.3 -1)

 

r = .0532

 

Interest rate is 5.32%

 

Check by plugging the interest rate into the compound formula

to determine if the equation balances

2600 = 2000(1+.0532/2)¹⁰

            2600 = 2600.41

 

Since the interest rate was rounded, I would say 5.32% is correct

 

 

Answer 2

Let the yearly rate of interest be r.

⇒ 2600 = 2000 (1 + r/200)¹⁰

⇒ r = 5.32%