Financial maths question Help!!

Question

Assume that you are going to retire in 25 years time.
You want a mortgage of $100000 now to extend and renovate your house but want to have it paid in full before you retire. The maximum repayment per month your budget will allow is $800. Using "trial and error", what is the rate of interest you need from your bank to have the loan repaid in 300 monthly payments (i.e 25 Years)?

Answer 1

What is your question? What do you not understand? Assigning your problems for others to solve is not helping you learn. You have to make an effort to show that you are at least attempting a solution. Show your work.

You can solve this with a financial calculator which is much faster and simpler than using formulas, and you can also use a spreadsheet function. But you have to understand annuities and compound interest before you start using a calculator.

 

Let's look at what we have

 

PV 100,000

N = 25 years = 300 months

PMT = 800 per month

FV = 0

i% = ?

 

Using trial and error, you assume some rate, say 7%, solve, and then adjust your rate higher or lower to approach the numbers above. but a calculator gives us the solution.

 

Assuming 7% interest (.58333% per month), you payment would be only$707. At 8% the payment is $772, which is getting much closer to your $800 limit. At 9% the payment is $839 so now you know that you can tolerate a rate between 8 and 9 percent. Continuing with 8.5 percent, and so on you can narrow it down to the actual rate of 8.42%. If you bank charges less, you can afford the mortgage, and it will be paid off before you retire.