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Chapter 5: Q. 2 (page 324)

If you borrow \(5000 and, after 9 months, pay off the loan in the amount of \)5500, what per annum rate of interest was charged?

Short Answer

Expert verified

Thus, the rate of interest per annum is13.3%.

Step by step solution

01

Step 1. Given information

The money borrowed, Principal P=$5000

The actual time that the money is borrowed must be expressed in years t=9months=912=34

The total amount paid, A=$5500

We have to find the rate of interest rper annum.

02

Step 2. Find interest 

We know that,

Amount = Principal + Interest

A=P+I

Put the given values and find I

$5500=$5000+I$5500-$5000=I$500=I

Thus, Interest charged is $500.

03

Step 3. Use simple interest formula and find r.

If a principal of Pdollars is borrowed for a period of tyears at a per annum interest rate r, expressed as a decimal, the interest Icharged is I=Ptr100

To find r, rate of interest per annum

r=IPt脳100

Substitute the values and simplify

r=5005000脳34脳100r=500脳100脳45000脳3r=403r=13.3%

Thus, the rate of interest per annum is13.3%.

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