Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9690

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 = $9690 – $5100 = $4590

Thus, Simple Interest = $4590

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 × 4590}/_{5100 × 10}

= ⁴⁵⁹⁰⁰⁰/₅₁₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5100

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4590 (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 = 10% of Principal

= 10% of $5100

= ¹⁰/₁₀₀ × 5100

= ^{10 × 5100}/₁₀₀

= ⁵¹⁰⁰⁰/₁₀₀ = 510

Thus, simple Interest for 1 year = $510

Now,

∵ If the simple Interest is $510, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₀ years

∴ If the simple Interest is $4590, then the time = ¹/₅₁₀ × 4590 years

= ^{1 × 4590}/₅₁₀ years

= ⁴⁵⁹⁰/₅₁₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.

(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?

(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(5) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.

(7) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.

(9) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.