Question

Bonnie has decided to begin a retirement savings program where she will contribute to an account that will accumulate tax free throughout her working life. She expects to retire in exactly 12 years from today, and her goal is to have accumulated the amount of $300000 when she reaches her future retirement age.

Answer 1

Answer:

This question is incomplete since the interest rate is not included and so is the requirement.  However, if it asking for the annual contributions Bonnie can make, you can calculate it as shown below and assuming a discount rate of 10%;

Explanation:

Since Bonnie's goal is $300,000, this will be the future value and you can use a financial calculator to solve for recurring deposits (PMT);

Time to retirement; N = 12

Interest rate; I/Y = 10%

Future value; FV = 300,000

One time present cashflow; PV = 0

then compute the recurring deposits; CPT PMT = 14,028.995

Therefore, she will need to contribute $14,029 every year to meet her goal.

Answer 2

The annual contribution to be made by Bonnie to reach the accumulated amount of $300,000 after 12 years is $149,090.

What is Present value?

The present value can be defined as the current value of the future cash flow at a specific interest rate.

To calculate the yearly contribution, we need to find the present value of $300,000 at the rate of 6% per annul.

The formula to calculate present value is:

$\rm PV = FV \dfrac{1}{(1 +r)^n}$, where PV is the present value, FV is the future value, r is the rate of interest and n is the number of periods.

The present value of $300,000 can be calculated as follows:

Given:

Future value is $300,000

Rate is 6%

Number of years is 12 years.

$\rm PV = FV \dfrac{1}{(1 +r)^n}\\\\\rm PV =\ 300,000\times \dfrac{1}{(1 +0.06)^{12}}\\\\\rm PV = \ 300,000 \times\dfrac{1}{2.0122}\\\\\rm PV = \ 300,000 \times 0.497\\\\\rm PV = \ 149,090$

Therefore the annual contribution should be $149,090.

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