Compound value solving for n​) How many years will the following​ take? a. ​$ to grow to ​$ if invested at percent compounded annually b. ​$ to grow to ​$ if invested at percent compounded annually c. ​$ to grow to ​$ if invested at percent compounded annually d. ​$ to grow to ​$ if invested at percent compounded annually

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A = P(1+r/100)^n Where A is future value, P is present value, r is rate of interest and n is time period  

1. A = P(1+r/100)^n

1042.51 = 480(1.09)^n

(1042.51/480) = 1.09^n

Taking log on both sides

log(1042.51/480) = n*log 1.09

n = log(1042.51/480)/log 1.09

n = 9 years.

2. A = P(1+r/100)^n

53.26 = 31(1.07)^n

(53.26/31) = 1.07^n

Taking log on both sides

log(53.26/31) = n*log 1.07

n = log(53.26/31)/log 1.07

n = 8 years

3. A = P(1+r/100)^n

383.59 = 100(1.13)^n

(383.59/100) = 1.13^n

Taking log on both sides

log(383.59/100) = n*log 1.13

n = log(383.59/100)/log 1.13

n = 11 years.

4. A = P(1+r/100)^n

66.91 = 53(1.06)^n

(66.91/53) = 1.06^n

Taking log on both sides

log(66.91/53) = n*log 1.06

n = log(66.91/53)/log 1.06

n = 0.10121516027 / 0.025306

n = 3.9997

n = 4 years.

When you reconcile your business bank account, you compare your internal financial records against the records provided to you by your bank. A monthly reconciliation helps you identify any unusual transactions that might be caused by fraud or accounting errors, and the practice can also help you spot inefficiencies.