Question

GC - If the principal amount of money put into a bank is $2000 with a 3.5% rate compounded quarterly, what is the amount after 6 years?

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Answer 1

Given:

Principal amount = $2000

Rate of interest = 3.5% compounded quarterly.

Time = 6 years

To find:

The amount after 6 years.

Solution:

The formula for amount after compound interest is:

`A=P\left(1+(r)/(n)\right)^(nt)`

Where, P is principal, r is rate of interest in decimal, n is the number of time interest compounded in an year and t is the number of years.

The interest is compounded quarterly, so
`n=4`.

Substituting
`P=2000,r=0.035,n=4,t=6`, we get

`A=2000\left(1+(0.035)/(4)\right)^(4(6))`

`A=2000\left(1+0.00875\right)^(24)`

`A=2000\left(1.00875\right)^(24)`

`A=2465.10340`

Approximate the value to the nearest hundredth.

`A\approx 2465.10`

The amount after 6 years us $2465.10. Therefore, the correct option is A.