Question

You will deposit $150 each of the next five years (the first deposit will occur one year from today, and there will be a total of 5 equal deposits) into an account that pays a 6.8% effective annual rate.  Six years from today, you wish to have exactly $1000 in the account. You would need to deposit an additional $_______ into the account six years from today to meet that goal. [Hints: Make a timeline! There are many ways to solve this problem, so you should be able to verify your answer by trying a different solution method. I recommend making sure you can solve this problem by starting it as an annuity problem.]

Do not round any intermediate work. Round your final answer to 2 decimal places (ex: if your answer is 12.345678 then you should enter 12.35). Margin of error for correct answers: +/- .05.

Answer 1

The formula to calculate accumulated value of equal annual deposits is given below:

Future value = Cash flow x- Futwe value – Cash flow x (7)=1

The amount to be deposited in 6 years is calculated below:

1,000 =150 x - X(1+0.068) + Additional amount 0.068 (1.389492681-1 1,000 =150 068) + Additional amount 0.068 1,000 =1505.727833541x(1.068) + Additional amount 1,000 =917.5989+ Additional amount 1,000-917.5989 = Additional amount 82.40 = Additional amount