Question

Jasmine has started a new job which allows her to invest money into a retirement savings account. She is given two options for her retirement account structure. Determine which account is the preferred option if she invests $2700 into it, and does not add any money to it for 15 years. a) Option A: A fixed annual interest rate of 9% compounded continuously. b) Option B: A annual interest rate of 9.8% compounded bimonthly.

Answer 1

Explanation:

To determine the preferred option, we need to calculate the future value of each account after 15 years.

For option A, the formula to calculate the future value is:

FV = P*e^(rt)

Where:

P = Principal amount = $2700

r = Annual interest rate = 9%

t = Time period = 15 years

Plugging in the values, we get:

FV = $2700*e^(0.09*15)

FV = $2700*e^1.35

FV = $2700*3.862

FV = $10,427.40

So, the future value of option A after 15 years is $10,427.40.

For option B, the formula to calculate the future value is:

FV = P*(1+(r/n))^(nt)

Where:

P = Principal amount = $2700

r = Annual interest rate = 9.8%

n = Number of times interest is compounded per year = 6 (bimonthly means twice a month, so 12/2 = 6)

t = Time period = 15 years

Plugging in the values, we get:

FV = $2700*(1+(0.098/6))^(6*15)

FV = $2700*(1+0.016333)^90

FV = $2700*2.456

FV = $6,634.93

So, the future value of option B after 15 years is $6,634.93.

Therefore, the preferred option is option A, with a future value of $10,427.40 after 15 years.