Simple Interest
MCQs Math


Question:     Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $12730

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 = $12730 – $6700 = $6030

Thus, Simple Interest = $6030

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 × 6030/6700 × 9

= 603000/60300

= 10 years (using formula)

Thus, Time (T) = 10 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) = $6700

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $6030 (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 = 9% of Principal

= 9% of $6700

= 9/100 × 6700

= 9 × 6700/100

= 60300/100 = 603

Thus, simple Interest for 1 year = $603

Now,

∵ If the simple Interest is $603, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/603 years

∴ If the simple Interest is $6030, then the time = 1/603 × 6030 years

= 1 × 6030/603 years

= 6030/603 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.

(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.

(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?


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