Question

Zelda borrowed R5760,00

 from a bank for 21 months. For the discount loan she only received R4752,00

. Determine: 

    (i)   the yearly discount rate, d

    (ii)   the equivalent yearly simple interest rate, i

Give the answers as percentages and round them to two decimal places.

Answer 1

In this we have to calculate present value on based on discount rate.

i

Discounted value = Present value=475200

Borrowed amount =576000

Period = 21 months =1.75 years 

r = Annual rate of interest

$Present\space value = \frac{Future\space value}{(1+r)^{1.75}}$

$475200=\frac{576000}{(1+r)^{1.75}}$

$(1+r)^{1.75}=1.2121212121$

r=11.62%

This is annual rate of interest.

ii

$Simple\space discount rate = \frac{Discount}{ borrowed\space amount }\times\frac{ 12\space months}{ Loan \space period }$

Discount =576000-475200=$100800

Simple interest rate $=\frac{101800}{576000} \times \frac{12}{21}=10\%$

Simple interest rate=10%