Question

Application 11. Dasha took out a loan of $500 in oeder to buy the # 1 selling book in the world, "Math, What is it Good For?" by Smart E. Pants. She plans to pay back this loanin 30 months. The loan will collect simple interest at 6.5% per year. How much will Dasha have to pay back at the end of this time? What is the accumulated interest? [3 marks]

Answer 1

`\boxed{\text{\$581.25; \$81.25}}`

Explanation:

The formula for the total accrued amount is

A = P(1 + rt)

Data:

P = $500

r = 6.5 % = 0.065

t = 30 mo

Calculations:

(a) Convert months to years

t = 30 mo × (1 yr/12 mo) = 2.5 yr

(b) Calculate the accrued amount

A = 500(1 + 0.065 × 2.5)

= 500(1 + 0.1625)

= 500 × 1.1625

= 581.25

`\text{Dasha will have to pay back }\boxed{\textbf{\$581.25}}`

(c) Calculate the accumulated interest

`\begin{array}{rcl}A & = & P + I\\581.25 & = & 500 + I\\I & = & 81.25\\\end{array}\\\text{The accumulated interest is }\boxed{\textbf{\$81.25}}`