Assume that your parents wanted to have $ 170 000$170 000 saved for university by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 10.5 %10.5% per year on their investments. a. How much would they have to save each year to reach their goal? b. If they think you will take four years instead of three to graduate and decide to have $ 220 000$220 000 saved just in case, how much would they have to save each year to reach their new goal?
Question
Assume that your parents wanted to have 170 000 saved for university by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 10.5 %10.5% per year on their investments. a. How much would they have to save each year to reach their goal? b. If they think you will take four years instead of three to graduate and decide to have 220 000 saved just in case, how much would they have to save each year to reach their new goal?
Solution
a. To calculate how much they would have to save each year to reach their goal, we can use the formula for the future value of a series of payments or annuities:
FV = P * [(1 + r)^n - 1] / r
where: FV = future value ($170,000) P = annual payment (what we're trying to find) r = interest rate (10.5% or 0.105) n = number of years (18 - 1 = 17)
Rearranging the formula to solve for P gives us:
P = FV * r / [(1 + r)^n - 1]
Substituting the given values into the formula gives us:
P = 17,850 / 46.022 P = $388.02
So, they would have to save approximately $388.02 each year to reach their goal.
b. If they want to have $220,000 saved instead, we can use the same formula and process to find the new annual payment:
P = 23,100 / 46.022 P = $501.71
So, they would have to save approximately $501.71 each year to reach their new goal.
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