Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4500

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7650

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 = $7650 – $4500 = $3150

Thus, Simple Interest = $3150

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 × 3150}/_{4500 × 7}

= ³¹⁵⁰⁰⁰/₃₁₅₀₀

= 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) = $4500

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3150 (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 = 7% of Principal

= 7% of $4500

= ⁷/₁₀₀ × 4500

= ^{7 × 4500}/₁₀₀

= ³¹⁵⁰⁰/₁₀₀ = 315

Thus, simple Interest for 1 year = $315

Now,

∵ If the simple Interest is $315, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₅ years

∴ If the simple Interest is $3150, then the time = ¹/₃₁₅ × 3150 years

= ^{1 × 3150}/₃₁₅ years

= ³¹⁵⁰/₃₁₅ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(2) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(4) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?

(5) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(6) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(9) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.