Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $7498

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 = $7498 – $4600 = $2898

Thus, Simple Interest = $2898

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 × 2898}/_{4600 × 7}

= ²⁸⁹⁸⁰⁰/₃₂₂₀₀

= 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) = $4600

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

Simple Interest = $2898 (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 $4600

= ⁷/₁₀₀ × 4600

= ^{7 × 4600}/₁₀₀

= ³²²⁰⁰/₁₀₀ = 322

Thus, simple Interest for 1 year = $322

Now,

∵ If the simple Interest is $322, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₂ years

∴ If the simple Interest is $2898, then the time = ¹/₃₂₂ × 2898 years

= ^{1 × 2898}/₃₂₂ years

= ²⁸⁹⁸/₃₂₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(2) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(4) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(5) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.

(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.

(8) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.

(9) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?