Question

Robert borrows $1000 for 8 months from a lender who charges a 16% discount rate. What size of loan should robert ask for so as to receive $1000 in cash? What is the equivalent simple interest rate he pays on the loan?

Answer 1

A) We can calculate the desired result as follows:

Amount Borrowed = $ 1,000

Period = 8 months

Discount / Interest rate = 16%

Amount received = Amount Borrowed - (Amount Borrowed * Discount / Interest rate * ( 8 / 12 ))

= 1,000 - (1,000 * 16% * ( 8 / 12 ))

= 1,000 - 106.6667

= $ 893.33

So, the amount robert will receive is $ 893.33

To receive $ 893.33 robert has to borrow $ 1,000

To receive $ 1,000 then robert has to borrow:

= ( 1,000 / 893.33 ) * 1,000

= 1.11940716 * 1,000

= $ 1,119.407

So, in order to receive $ 1,000 robert has to borrow $ 1,119.407

B) Equivalent simple interest is calculated as follows:

Simple Interest = Amount received* Annual Interest rate * period

1,000 * 16% * ( 8 / 12 ) = 893.33 * Annual Interest rate * ( 8 / 12 )

106.6667 = 893.33 * Annual Interest rate * ( 8 / 12 )

106.6667 / 595.55533 = Annual Interest rate

Annual Equivalent Interest rate = 0.1791 or 17.91%