Yumi's grandparents presented her with a gift of $11,000 when she was 8 years old to be used for her college education. Over the next 9 years, until she turned 17, Yumi's parents had invested her money in a tax-free account that had yielded interest at the rate of 5.5%/year compounded monthly. Upon turning 17, Yumi now plans to withdraw her funds in equal annual installments over the next 4 years, starting at age 18. If the college fund is expected to earn interest at the rate of 7%/year, compounded annually, what will be the size of each installment?

Question

Yumi's grandparents presented her with a gift of $11,000 when she was 8 years old to be used for her college education. Over the next 9 years, until she turned 17, Yumi's parents had invested her money in a tax-free account that had yielded interest at the rate of 5.5%/year compounded monthly. Upon turning 17, Yumi now plans to withdraw her funds in equal annual installments over the next 4 years, starting at age 18. If the college fund is expected to earn interest at the rate of 7%/year, compounded annually, what will be the size of each installment?

Answer 1

finite math suxssssss

Answer 2

when Yumi turned 17, the fund was worth

11000(1+.055/12)^(12*9) = 18025.08

Now, plug that into your annuity formula, to get annual payments of

M = Pr/(1-(1+r)^(-n))
= 18025.08(1-(1.07)^-4)
= 4273.83

Answer 3

234+323

34243
+2
=69

Answer 4

To find the size of each annual installment, we need to calculate the value of Yumi's college fund at age 17 (after 9 years of investment) and then calculate the annuity payment based on the future value.

First, let's calculate the future value of Yumi's college fund at age 17. We can use the compound interest formula:

FV = PV * (1 + r/n)^(n*t)

Where:
FV is the future value
PV is the present value (initial investment)
r is the annual interest rate
n is the number of times interest is compounded per year
t is the number of years

PV = $11,000
r = 5.5% = 0.055
n = 12 (compounded monthly)
t = 9 years

Calculating the future value:

FV = $11,000 * (1 + 0.055/12)^(12*9)
FV ≈ $15,440.56

The college fund's value at age 17 is approximately $15,440.56.

Now, let's calculate the size of each equal annual installment using the future value and the annuity formula:

PV = FV
r = 7% = 0.07
n = 1 (compounded annually)
t = 4 years

Using the annuity formula:

PV = PMT * [(1 - (1 + r)^-n) / r]

Where:
PMT is the size of each equal annual installment

$15,440.56 = PMT * [(1 - (1 + 0.07)^-4) / 0.07]

Simplifying the equation:

$15,440.56 = PMT * [(1 - 0.68301) / 0.07]
$15,440.56 = PMT * [0.31699 / 0.07]
$15,440.56 = PMT * 4.52843

Dividing both sides by 4.52843:

PMT ≈ $3,409.09

Therefore, the size of each annual installment Yumi can withdraw over the next 4 years will be approximately $3,409.09.