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Simple Interest
Math MCQs


Question :    Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $9394

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 = $9394 – $6100 = $3294

Thus, Simple Interest = $3294

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 × 3294/6100 × 9

= 329400/54900

= 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) = $6100

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

Simple Interest = $3294 (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 $6100

= 9/100 × 6100

= 9 × 6100/100

= 54900/100 = 549

Thus, simple Interest for 1 year = $549

Now,

∵ If the simple Interest is $549, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/549 years

∴ If the simple Interest is $3294, then the time = 1/549 × 3294 years

= 1 × 3294/549 years

= 3294/549 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(2) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(3) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.

(5) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.

(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?

(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.

(10) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.