Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $10010

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 = $10010 – $6500 = $3510

Thus, Simple Interest = $3510

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 × 3510}/_{6500 × 9}

= ³⁵¹⁰⁰⁰/₅₈₅₀₀

= 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) = $6500

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

Simple Interest = $3510 (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 $6500

= ⁹/₁₀₀ × 6500

= ^{9 × 6500}/₁₀₀

= ⁵⁸⁵⁰⁰/₁₀₀ = 585

Thus, simple Interest for 1 year = $585

Now,

∵ If the simple Interest is $585, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₈₅ years

∴ If the simple Interest is $3510, then the time = ¹/₅₈₅ × 3510 years

= ^{1 × 3510}/₅₈₅ years

= ³⁵¹⁰/₅₈₅ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?

(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(4) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.

(6) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(8) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.