SOLUTION: Mateo and Klaus would like to buy a house and their dream starter home costs $650,000. Their goal is then to save $65,000 for a down payment and then would take out a mortgage loa

Question 1208431: Mateo and Klaus would like to buy a house and their dream starter home costs $650,000. Their goal is then to save $65,000 for a down payment and then would take out a mortgage loan for the rest. They plan to put their monthly saved amount in a conservative mutual fund that has a track record of a 4.25% rate of return, compounded quarterly. To break it into managebale amounts, they are going to deposit into their savings every week. Their hope is to be able to buy this home in 7 years.
What would their weekly savings amount have to be to reach this goal? [Blank-1]
What will be the total interest earned? [Blank-2]
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to calculate the weekly savings amount and total interest earned:
**1. Calculate the quarterly interest rate:**
* Annual interest rate: 4.25% = 0.0425
* Quarterly interest rate: 0.0425 / 4 = 0.010625
**2. Calculate the total number of compounding periods:**
* Number of years: 7
* Compounding periods per year: 4
* Total compounding periods: 7 * 4 = 28
**3. Use the future value of an ordinary annuity formula:**
The future value (FV) of an ordinary annuity is the total value of a series of equal payments (in this case, weekly savings) at the end of each period, with interest accumulating over time. The formula is:
FV = P * [((1 + r)^n - 1) / r]
Where:
* FV = Future Value ($65,000 down payment)
* P = Periodic payment (weekly savings - what we need to find)
* r = Interest rate per period (quarterly rate)
* n = Number of periods (number of quarters)
Since we are saving weekly and interest is compounded quarterly, we need to adjust the formula a bit. We'll consider the total amount saved over the 7 years as the total amount of the annuity, and solve for the weekly payment.
**4. Adjust and solve for the weekly payment (P):**
Since contributions are weekly and compounding is quarterly, we can approximate the future value formula to solve for weekly contributions.
FV ≈ P * weeks per year * years * (((1 + r)^n - 1) / r)
$65,000 ≈ P * 52 * 7 * (((1 + 0.010625)^28 - 1) / 0.010625)
$65,000 ≈ P * 364 * (32.539)
$65,000 ≈ P * 11,843.27
P ≈ $65,000 / 11,843.27
P ≈ $5.49 per week
**5. Calculate the total amount saved:**
* Weekly savings: $5.49
* Weeks per year: 52
* Number of years: 7
* Total saved: $5.49 * 52 * 7 = $2002.36
**6. Calculate the total interest earned:**
* Down payment goal: $65,000
* Total saved: $2002.36
* Total interest earned: $65,000 - $2002.36 = $62,997.64
**Answer:**
* *:** Their weekly savings amount would have to be approximately $5.49.
* *:** The total interest earned would be approximately $62,997.64.

RELATED QUESTIONS
Aya and Sakura would like to buy a house and their dream home costs $500,000. Their goal (answered by Theo,MathTherapy)

1- Aya and Harumi would like to buy a house and their dream house costs $500,000. They... (answered by Theo)

Aya and Harumi would like to buy a house and their dream house costs $500,000. They have (answered by CPhill)

You are tasked with assisting a young couple in purchasing a home. The couple wants to... (answered by Theo,ikleyn)

1.Betty, who has just started her first full-time salary job is determined to have $1... (answered by addingup,MathTherapy)

1.Marina had an accident with her car and the repair bill came to $800. She didn�t have... (answered by ikleyn)

Please help me with this problem. Your parents are planning to retire in 18 years.... (answered by stanbon)

TL Ltd is a multinational construction company with subsidiary organisations all around... (answered by ikleyn)

A farmer in the Midwest has 1,000 acres of land on which she intends to plant corn,... (answered by ikleyn)