Question

AutoSave OFE DE S U S A = Ass... - Saved... Qu Search in Document lome Insert Draw Design Layout References Mailings Share Comments Calibri (Bo... 11 A A A A BIUab x x AAA Paste SE SE Styles Styles Pane Assignment for Bonus Points 1. You want to have a nest egg of $2 million when you retire 25 years from today. Assuming an annual return of 5%, how much must you save annually to achive your target?

Answer 1

Here, the savings to be made will be same every year, so it is an annuity. To calculate the amount of savings each year, we will use the following formula of future value of annuity:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity = $2m or $2000000, P is the periodical amount, r is the rate of interest = 5% and n is the time period = 25

Now, putting these values in the above formula, we get,

$2000000 = P * ((1 + 5%)²⁵ - 1 / 5%)

$2000000 = P * ((1 + 0.05)²⁵ - 1 / 0.05)

$2000000 = P * ((1.05)²⁵ - 1 / 0.05)

$2000000 = P * ((3.3863549409- 1) / 0.05)

$2000000 = P * (2.3863549409/ 0.05)

$2000000 = P * 47.727098818

P = $2000000 / 47.727098818

P = $41904.91

So, $41904.91 must be saved annually to achieve the target.