Question

A property was purchased for $10,000.00 down and quarterly payments of $1,350 for 10 years. If the first payment was made on the date of the purchase and interest is 5.5 % compounded quarterly, a. what was the purchase price of the property? b. how much is the cost of financing? C. what is the effective rate of interest equivalent to a nominal rate of 5.5 % compounded quarterly?

Answer 1

cost of financing is $12108.62

interest is 5.614 %

Explanation:

given data

payment = $10000

principal = $1350

time t = 10 year = 10 × 4 = 40

rate r = 5.5 % = 5.4 /4 = 1.375 %

to find out

purchase price and cost of financing and rate of interest

solution

we know here purchase price is calculated as

purchase price = payment + present value .................1

present value = principal (1+r) ( 1-
`(1+r)^(-t)` / r )

put here value

present value = 1350 (1+0.1375) ( 1-
`(1+01375)^(-40)` / 0.01375 )

present value = 41891.3833

so from equation 1

purchase price = 10000 + 41891.3833

purchase price = $51891.38

and

so amount of payment is here

amount of payment = 10000 + 40×1350

amount of payment = $64000

so here cost of financing is here

cost of financing = 64000 - 51891.38

cost of financing = $12108.62

and

so here

1 + interest =
`(1+0.055/4)^(4)`

1 + interest =
`(1.01375)^(4)`

interest = 0.0561448

interest = 5.614 %