plz explain how you solve 550(1+x/100)^10=638.30 (compound interest)

Question

 plz explain

Answer 1

It appears you are looking for the interest rate earned when

one invests $550 for 10 years at an interest rate of x%

compoundd annually with a final total of $638.30

 

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

A= final value = $638.30

p= principal = $550

r = interest rate = x/100

n= number times compounded per year=1

t = time in years = 10

 

638.3 = 550(1 + x/100)¹⁰

 

638.3/550 = (1 + x/100)¹⁰

 

Take the 10th root of both sides

 

¹⁰√(638.3/550) = 1 + x/100

 

 A scientific calculator using ^y√x gives:

 

1.015 = 1 + x/100

 

subtract 1 from both sides

 

0.015 = x/100

 

multiply both sides by 100

 

x = 1.5

 

The annual percentage rate is 1.5%

*******************************

 

Check:

550(1 + 1.5/100)¹⁰ = 550(1.015)¹⁰ = $638.30

 

Answer matches and is correct.

 

Answer 2

550(1+0.01x)¹⁰ = 638.30

 

(1+0.01x)¹⁰ = 1.1605

 

log(1+0.01x)¹⁰ = log(1.1605)

 

10[log(1+0.01x)] = 0.06466

 

log(1+0.01x) = 0.006466

 

1+0.01x = 10^0.006466

 

    0.01x = 0.014999

 

          x = 1.499