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Simple Interest
Math MCQs


Question :    Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7208

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7208 – $5300 = $1908

Thus, Simple Interest = $1908

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = 100 × Simple Interest/Principal × Rate of Interest

⇒ T = 100 × SI/P × R

Thus, Time (T) = 100 × 1908/5300 × 6

= 190800/31800

= 6 years (using formula)

Thus, Time (T) = 6 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5300

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1908 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 6% of Principal

= 6% of $5300

= 6/100 × 5300

= 6 × 5300/100

= 31800/100 = 318

Thus, simple Interest for 1 year = $318

Now,

∵ If the simple Interest is $318, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/318 years

∴ If the simple Interest is $1908, then the time = 1/318 × 1908 years

= 1 × 1908/318 years

= 1908/318 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.

(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.

(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?

(8) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(9) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.