Question

Your uncle will sell you his bicycle shop for $170,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be?

Answer 1

Answer:

A loan payment calculator provides the information you need when deciding whether or not you can afford to borrow money.

In the above question, it's my job to see how much I need to pay my uncle if I borrowed $170,000 from him at an annual interest rate of 6%.

I'm supposed to payback monthly over the next 4 years.

Given the above, my monthly payment is computed as follows:

STEP I - Define Formula and Variables

Note firstly that the monthly payments are in instalments.

Formula:  

               

(P x I) x ((1 + r)n)/ (t x ((1 + r)n)- 1)

P is the principal amount borrowed,

I is the annual interest rate,

r is the periodic monthly interest rate,

n is the total number of monthly payments, and t is the number of months in a year.

 

P: $170,000, the amount of the loan

r: 0.005 (6% annual rate—expressed as 0.06—divided by 12 monthly payments per year)

n: 48 (12 monthly payments per year times 4 years)

STEP II - Insert Variables

Inserting our given information we have:

= ($170,000 + ($170,000 x 4 x 0.005)) / (4 x 12)

STEP III - Simplify

Simplified further we have

= ($170,000+$3400)/48

= $173,400/48

= $3,612.5

So equal monthly payments would be equal to

= $3,612.5

Cheers!

Answer 2

Answer:

The equal monthly payment is $3,068.20  

Explanation:

The equally monthly payments can be computed using the pmt formula in excel.

=pmt(rate,nper,pv,fv)

rate is the monthly nominal rate of 6%/12=0.5%

nper is the number of monthly payments required which is 4*12=48

pv is the current value of the bicycle of $170,000

fv is the worth balance of the financing arrangement at the end of fourth year that should be paid once ,$50,000 balloon payment

=pmt(0.5%,48,-170000,50000)

=$3,068.20  

Note that the interest is one month interest rate as the payment is expected monthly.