Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $7644

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 = $7644 – $4900 = $2744

Thus, Simple Interest = $2744

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 × 2744}/_{4900 × 7}

= ²⁷⁴⁴⁰⁰/₃₄₃₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4900

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

Simple Interest = $2744 (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 $4900

= ⁷/₁₀₀ × 4900

= ^{7 × 4900}/₁₀₀

= ³⁴³⁰⁰/₁₀₀ = 343

Thus, simple Interest for 1 year = $343

Now,

∵ If the simple Interest is $343, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₃ years

∴ If the simple Interest is $2744, then the time = ¹/₃₄₃ × 2744 years

= ^{1 × 2744}/₃₄₃ years

= ²⁷⁴⁴/₃₄₃ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?

(2) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.

(4) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.

(8) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.