Yumi's grandparents presented her with a gift of $12,000 when she was 10 yr old to be used for her college education. Over the next 7 yr, 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 yr, starting at age 18. If the college fund is expected to earn interest at the rate of 6%/year, compounded annually, what will be the size of each installment? (Assume no interest is accrued from the point she turns 17 until she makes the first withdrawal. Round your answer to the nearest cent.)

Question

Yumi's grandparents presented her with a gift of $12,000 when she was 10 yr old to be used for her college education. Over the next 7 yr, 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 yr, starting at age 18. If the college fund is expected to earn interest at the rate of 6%/year, compounded annually, what will be the size of each installment? (Assume no interest is accrued from the point she turns 17 until she makes the first withdrawal. Round your answer to the nearest cent.)

Answer 1

A certain drug leaves the bloodstream at a rate of 22% per hour. If you are given an initial dose of 20 mg, how long until there are 10 mg in your bloodstream?

Answer 2

To find the size of each installment, we can follow these steps:

Step 1: Calculate the accumulated amount of money in Yumi's college fund when she turns 17.
Given:
Principal amount (P) = $12,000
Annual interest rate (r) = 5.5%
Compounding frequency (n) = 12 (monthly compounding)
Time period (t) = 7 years

Using the compound interest formula: A = P(1 + r/n)^(nt)
A = 12,000(1 + 0.055/12)^(12 * 7)
A ≈ $16,596.35 (rounded to the nearest cent)

Step 2: Calculate the size of each installment over 4 years.
Given:
Principal amount (P) = $16,596.35
Annual interest rate (r) = 6%
Compounding frequency (n) = 1 (annually)
Time period (t) = 4 years

Using the future value of an annuity formula with regular deposits: FV = P * [(1 + r)^t - 1] / r
FV = 16,596.35 * [(1 + 0.06)^4 - 1] / 0.06
FV ≈ $5,968.10 (rounded to the nearest cent)

Step 3: Calculate the size of each annual installment.
Since Yumi will withdraw the funds in equal annual installments over 4 years, the size of each installment will be the total accumulated amount divided by the number of installments.
Installments = FV / t
Installments = 5,968.10 / 4
Installments ≈ $1,492.03 (rounded to the nearest cent)

Therefore, the size of each annual installment for Yumi's college fund will be approximately $1,492.03.