Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6512

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 = $6512 – $4400 = $2112

Thus, Simple Interest = $2112

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 × 2112}/_{4400 × 6}

= ²¹¹²⁰⁰/₂₆₄₀₀

= 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) = $4400

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2112 (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 = 6% of Principal

= 6% of $4400

= ⁶/₁₀₀ × 4400

= ^{6 × 4400}/₁₀₀

= ²⁶⁴⁰⁰/₁₀₀ = 264

Thus, simple Interest for 1 year = $264

Now,

∵ If the simple Interest is $264, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₆₄ years

∴ If the simple Interest is $2112, then the time = ¹/₂₆₄ × 2112 years

= ^{1 × 2112}/₂₆₄ years

= ²¹¹²/₂₆₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.

(2) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?

(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?

(5) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?

(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

(9) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.