Find the time required for an investment of 5000 dollars to grow to 6100 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

The time (t) = 2.6 years

Step-by-step explanation:

To calculate the time for earning a compound interest, compounded on a certain amount of present value (PV), compounded periodically, the following formula is used:

where:

FV = future value = $6,100

PV = present value = $5,000

i = interest rate in decimal = 7.5% = 0.075

n = number of compounding periods per year = quarterly = 4 (4 quarters a year)

t = time of compounding in years = ???

Therefore the time is calculated thus:

Next, let us divide both sides of the equation by 5000

1.22 =

Taking natural logarithm of both sides

㏑(1.22) = ㏑

㏑(1.22) = 4t × ㏑(1.01875)

0.1989 = 4t × 0.01858

4t =

∴ 4t = 10.71

t = 10.71 ÷ 4 = 2.6 years

answer: 10 meter

step-by-step explanation:

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