Find how long it takes a $1000 investment to earn $200 interest at 7% interest compounded quarterly.

Question

Find how long it takes a $1000 investment to earn $200 interest at 7% interest compounded quarterly.

I am supposed to use the formula: A=P(1+ r/n)^nt

Answer 1

You just want to identify the variables in the formula and plug in the values given to solve for t. Keep in mind that the interest should be written as a decimal for the calculation and quarterly is 4 times per year.

Time, t is an exponent, so you will need utilize logarithms

The accumulation A is the Principal plus the $200 interest

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

A = 1200 = 200 + 1000

P= 1000

r = 7% written as .07 

n = 4

1200 = 1000(1 + .07/4)^4t

1200 = 1000(1 + 0.0175)^4t

1200 = 1000(1.0175)^4t

Divide both sides by 1000

1200/1000 = 1000(1.0175)^4t

1.2 = (1.0175)^4t apply logarithms here

As in log(y^x) = x(log y)

log 1.2 = 4t(log 1.0175)

log 1.2/4(log 1.0175) = t

2.62732 years = t

Checking

1200 = 1000(1 + .07/4)^4t

1200 = 1000(1 + .07/4)^4(2.62732)

1200 = 1000(1 + 0.0175)^4(2.62732)

1200 = 1000(1.0175)^4(2.62732)

1200 = 1000(1.2000) = 1200

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