A young family is looking to enter the property market. They plan to save for a 10% deposit and take out a loan (for the 90% balance). The deposit is for 10% of the property's value at the time the loan is taken out. The property is valued at $890,000 today, and is modelled to increase in value by 0.5% each month. The family can set aside $5,000 each month-end till the 10% deposit is made. The savings account pays interest at a rate of 0.5% each month. When the deposit is reached, a 30-year loan is taken out at an interest rate of 0.6% per month. a. Write the value, P(t) for the value of the property at the end of the tih month. b. Formulate a difference equation for the future value of the savings plan. c. Detail the finite difference solution for S(t), the future value of the savings plan. d. Solve for t, the time when the 10% deposit may be made and calculate the loan amount (to the nearest dollar). e. Detail the solution to calculate the monthly repayment amount (to the nearest cent).
A young family is looking to enter the property market. They plan to save for a 10% deposit and take out a loan (for the 90% balance). The deposit is for 10% of the property's value at the time the loan is taken out. The property is valued at $890,000 today, and is modelled to increase in value by 0.5% each month. The family can set aside $5,000 each month-end till the 10% deposit is made. The savings account pays interest at a rate of 0.5% each month. When the deposit is reached, a 30-year loan is taken out at an interest rate of 0.6% per month. a. Write the value, P(t) for the value of the property at the end of the tih month. b. Formulate a difference equation for the future value of the savings plan. c. Detail the finite difference solution for S(t), the future value of the savings plan. d. Solve for t, the time when the 10% deposit may be made and calculate the loan amount (to the nearest dollar). e. Detail the solution to calculate the monthly repayment amount (to the nearest cent).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A young family is looking to enter the property market. They plan to save for a 10% deposit and take out a loan (for the 90% balance). The deposit
is for 10% of the property's value at the time the loan is taken out.
The property is valued at $890,000 today, and is modelled to increase in value by 0.5% each month.
The family can set aside $5,000 each month-end till the 10% deposit is made. The savings account pays interest at a rate of 0.5% each month.
When the deposit is reached, a 30-year loan is taken out at an interest rate of 0.6% per month.
a. Write the value, P(t) for the value of the property at the end of the tih month.
b. Formulate a difference equation for the future value of the savings plan.
c. Detail the finite difference solution for S(t), the future value of the savings plan.
d. Solve for t, the time when the 10% deposit may be made and calculate the loan amount (to the nearest dollar).
e. Detail the solution to calculate the monthly repayment amount (to the nearest cent).
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