Assume that your parents wanted to have a 170,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 6.5% per year on their investmenets. Required:a. How much would they have to save each year to reach their goal?b. If they think you will take five years instead of four to graduate to graduate and decide to have $140,000 saved just in case, how much more would they have to save each year to reach their new goal?

a. They will have to save $5,245.28 each year to reach their goal of $170,000.

b. They will have to save $925.63 less to reach their new goal of $140,000.

Note: The answer to part b is based on the information in the question. Therefore, the correct answer is "they will have to save $925.63 less" not  "save more" as suggested in the question. Kindly confirm this from your teacher.

Explanation:

a. How much would they have to save each year to reach their goal?

Since the saving started on your first birthday to have $170,000 saved, it implies the saving will be on your every birthday for 18 years. Therefore, the relevant formula to use to determine this is the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = M * {[(1 + r)^n - 1] / r} (1)

Where,

FV = Future value of the amount after your 18th birthday = $170,000

M = Yearly saving to have $170,000 = ?

r = interest rate = 6.5%, 0.065

n = number of years this savings will be made = 18

Substituting the values into equation (1) and solve for M, we have:

$170,000 = M * {[(1 + 0.065)^18 - 1] / 0.065}

$170,000 = M * 32.4100673759666

M = $170,000 / 32.4100673759666

M = $5,245.28

Therefore, they will have to save $5,245.28 each year to reach their goal of $170,000.

b. If they think you will take five years instead of four to graduate to graduate and decide to have $140,000 saved just in case, how much more would they have to save each year to reach their new goal?

First, we have to calculate how much they will save each year, by also using the Future Value (FV) for calculating an Ordinary Annuity as follows:

FVn = Mn * {[(1 + r)^n - 1] / r} (1)

Where,

FV1 = New future value of the amount after your 18th birthday = $140,000

M1 = New yearly saving to have $140,000 = ?

r = interest rate = 6.5%, 0.065

n = number of years this savings will be made = 18

Substituting the values into equation (1) and solve for M1, we have:

$140,000 = M1 * {[(1 + 0.065)^18 - 1] / 0.065}

$140,000 = M1 * 32.4100673759666

M1 = $140,000 / 32.4100673759666

M1 = $4,319.65

Therefore, they will have to save $4,319.65 each year to reach their goal of $140,000.

To obtain difference in yearly savings, we have:

Difference in yealy saving = M - M1 = $5,245.28 - $4,319.65 = $925.63

Since $5,245.28 each year to reach their goal of $170,000 is greater than $4,319.65 each year to reach their goal of $140,000, it therefore implies that they will have to save $925.63 less to reach their new goal of $140,000.

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