Finding the Interest Rate

Question

Find the required annual interest rate to the nearest tenth of a percent for 65,000 to grow to 65,325 if interest is compounded monthly for 6 months.

 

This is what I think I know:

A = 65,325

P = 65,000

t = 0.5

 

65,325 = 65,000(1 + r/n)^(0.5)(n)

1.005 = (1 + r/n)^0.5(n)

 

n is where I get stuck. Would it be 6 for 6 months or 1 for monthly? Any help would be appreciated.

Answer 1

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

 

A = future or final amount = 65,325

p = principal = 65,000

r = interest rate = tbd

n = # times compounded per year = 12

t = time in years = 1/2 or 0.5

 

65325 = 65000(1+r/12)^12(.5)

 

1.005 = (1+r/12)⁶

⁶√1.005 = 1+r/12

 

⁶√1.005 - 1 = r/12

 

r = 12(⁶√1.005 - 1)

 

r = .00997923

 

r ≅ 1%

 

check:  65325 = 65000(1+.01/12)⁶

           65325 = 65325.68

This is certainly close enough as a rounded answer.