Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $11696

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 = $11696 – $6800 = $4896

Thus, Simple Interest = $4896

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 × 4896}/_{6800 × 8}

= ⁴⁸⁹⁶⁰⁰/₅₄₄₀₀

= 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) = $6800

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $4896 (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 = 8% of Principal

= 8% of $6800

= ⁸/₁₀₀ × 6800

= ^{8 × 6800}/₁₀₀

= ⁵⁴⁴⁰⁰/₁₀₀ = 544

Thus, simple Interest for 1 year = $544

Now,

∵ If the simple Interest is $544, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₄ years

∴ If the simple Interest is $4896, then the time = ¹/₅₄₄ × 4896 years

= ^{1 × 4896}/₅₄₄ years

= ⁴⁸⁹⁶/₅₄₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?

(5) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.

(8) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?

(10) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.