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 $6240 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $6240

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 = $6240 – $4000 = $2240

Thus, Simple Interest = $2240

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 × 2240}/_{4000 × 8}

= ²²⁴⁰⁰⁰/₃₂₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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 = $2240 (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 $2240, then the time = ¹/₃₂₀ × 2240 years

= ^{1 × 2240}/₃₂₀ years

= ²²⁴⁰/₃₂₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.

(2) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

(3) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(4) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?

(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.

(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(9) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?

(10) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?