Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $11524

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 = $11524 – $6700 = $4824

Thus, Simple Interest = $4824

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 × 4824}/_{6700 × 8}

= ⁴⁸²⁴⁰⁰/₅₃₆₀₀

= 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) = $6700

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

Simple Interest = $4824 (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 $6700

= ⁸/₁₀₀ × 6700

= ^{8 × 6700}/₁₀₀

= ⁵³⁶⁰⁰/₁₀₀ = 536

Thus, simple Interest for 1 year = $536

Now,

∵ If the simple Interest is $536, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₆ years

∴ If the simple Interest is $4824, then the time = ¹/₅₃₆ × 4824 years

= ^{1 × 4824}/₅₃₆ years

= ⁴⁸²⁴/₅₃₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.

(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?

(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?

(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(8) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(10) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.