Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $7568

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 = $7568 – $4400 = $3168

Thus, Simple Interest = $3168

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 × 3168}/_{4400 × 8}

= ³¹⁶⁸⁰⁰/₃₅₂₀₀

= 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) = $4400

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

Simple Interest = $3168 (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 $4400

= ⁸/₁₀₀ × 4400

= ^{8 × 4400}/₁₀₀

= ³⁵²⁰⁰/₁₀₀ = 352

Thus, simple Interest for 1 year = $352

Now,

∵ If the simple Interest is $352, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₂ years

∴ If the simple Interest is $3168, then the time = ¹/₃₅₂ × 3168 years

= ^{1 × 3168}/₃₅₂ years

= ³¹⁶⁸/₃₅₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

(2) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.

(5) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(6) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.

(7) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(8) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?

(9) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?

(10) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.