Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $6556

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 = $6556 – $4400 = $2156

Thus, Simple Interest = $2156

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 × 2156}/_{4400 × 7}

= ²¹⁵⁶⁰⁰/₃₀₈₀₀

= 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) = $4400

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

Simple Interest = $2156 (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 $4400

= ⁷/₁₀₀ × 4400

= ^{7 × 4400}/₁₀₀

= ³⁰⁸⁰⁰/₁₀₀ = 308

Thus, simple Interest for 1 year = $308

Now,

∵ If the simple Interest is $308, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₈ years

∴ If the simple Interest is $2156, then the time = ¹/₃₀₈ × 2156 years

= ^{1 × 2156}/₃₀₈ years

= ²¹⁵⁶/₃₀₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.

(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(6) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(7) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(8) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.

(10) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.