Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $7200

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 = $7200 – $4000 = $3200

Thus, Simple Interest = $3200

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 × 3200}/_{4000 × 8}

= ³²⁰⁰⁰⁰/₃₂₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $4000

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

Simple Interest = $3200 (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 $4000

= ⁸/₁₀₀ × 4000

= ^{8 × 4000}/₁₀₀

= ³²⁰⁰⁰/₁₀₀ = 320

Thus, simple Interest for 1 year = $320

Now,

∵ If the simple Interest is $320, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₀ years

∴ If the simple Interest is $3200, then the time = ¹/₃₂₀ × 3200 years

= ^{1 × 3200}/₃₂₀ years

= ³²⁰⁰/₃₂₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?

(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.

(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(7) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?

(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.

(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.