Keith opened an investment account where he is paid 8% annual interest, compounded semi-annually. He wants to have $7,000 in the investment account in 3 years. What is the number of periods for this investment?

6 periods

Step-by-step explanation:

The investment is compounded semi-annually which means it is compounded twice in a year. Period of investment is 3 years. So, number of periods compounded is 3 multiplied by 2 that is 6 periods.

Rate would be 8% divided by 2 that is 4%.

Initial investment can be calculated usinf spreadsheet function as =PV(rate,nper, pmt, FV)

Where,

rate is 0.04

nper is 6

pmt is 0

FV is 7,000

So, initial investment is $5,532.20.

It is negative as it is a cash outflow.

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!