A deposit of $160,000 is compounded monthly at an annual percentage rate of 6.75%. How long will it take for the money to triple?

Question

This is for one of my math questions. I need help ASAP

Answer 1

Hi Lolls,

 

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

r = 0.0675

n = 12 (number of times of compounding annually)

t = time in years

A = initial amount

P = final amount

 

480000 = 160000(1+(0.0675/12))^12t

3 = 1.005625^12t  (take log of both sides)

log 3 = log (1.005625^12t )

0.48 = 12t log (1.005625)

0.48 = 0.03t

t = 16 years

Answer 2

For periodic compounded interest, use the formula A = P(1 + r/n)^nt

 

where A is the accumulated amount, P is the beginning amount, r is the annual interest rate expressed as a decimal value, n is the number of compounding periods per year, and t is the number of years.

 

For this problem, P = 160,000, A = 3*P = 3*160,000 = 480,000, r = 0.0675, and n = 12.

 

Substituting the values into the equation gives:

 

480,000 = 160,000(1 + 0.0675/12)^12t

 

Dividing both sides by 160,000 leaves:

 

3 = (1 + 0.0675/12)^12t

 

Taking the natural logarithm of both sides gives:

 

ln(3) = 12t*ln(1 + .0675/12)

 

Solving for t then gives:

 

t = ln(3) / 12*ln(1 + 0.0675/12)

 

t = 16.32 years  (round off as needed)

 

 

Answer 3

the formula is A = P (1 + r/n)^nt where A = final amount P = original amount r = rate of increase n = number of increases per year t = number of years 480000 = 160000 (1 + 0.0675/12)^12t 3 = 1.0675^12t ln 3 = 12t x ln (1.005625) t = ln 3 / ln (1.005625) /12 = 16.32 years