Assume that your parents wanted to have $170,000 saved for college by your 18th
ID: 2817025 • Letter: A
Question
Assume that your parents wanted to have $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 investments. 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 and decide to have $210,000 saved just in case, how much would they have to save each year to reach their new goal? a. How much would they have to save each year to reach their goal? To reach the goal of $170,000, the amount they have to save each year is S(Round to the nearest cent)Explanation / Answer
An ordinary future annuity is a sequence where equal payments are made at equal intervals with a fixed rate of interest. The equation for the same is below:
a) GIven, the amount required at the end of 18th birthday or future valaue of investment, A= $170,000
Rate of interest r = 6.5% p.a
n is the number of payment = 18 as the first payment is made on the first birthday and the last payment on the 18th birthday
P = payment made at the end of each year
A = P*[ {(1+r)n-1}/i ]
170000 = P[{(1+0.065)18-1}/0.065]
170000 = P[{(1.065)18-1}/0.065]
P = 170000/32.41
= $5245.28
To reach the goal of $170,000, the amount they have to save each year is $5245.28
b) Similarly, now the total investment expected at the end of 18 years is $210,000 when the new estimated graduation years is five years instead of four years. The number of payment remains the same as they want a total investment of 210,000 at the end of 18th year.
Here, A = 210,000
r = 6.5%p.a
n = 18
A = P*[ {(1+r)n-1}/i ]
210,000= P[{(1+0.065)18-1}/0.065]
210,000 = P[{(1.065)18-1}/0.065]
P = 210,000/32.41
P = $6479.47
To reach the goal of $210,000, the amount they have to save each year is $6479.47.
No intermediate rounding is done.