Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $8046

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 = $8046 – $5400 = $2646

Thus, Simple Interest = $2646

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 × 2646}/_{5400 × 7}

= ²⁶⁴⁶⁰⁰/₃₇₈₀₀

= 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) = $5400

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

Simple Interest = $2646 (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 $5400

= ⁷/₁₀₀ × 5400

= ^{7 × 5400}/₁₀₀

= ³⁷⁸⁰⁰/₁₀₀ = 378

Thus, simple Interest for 1 year = $378

Now,

∵ If the simple Interest is $378, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₈ years

∴ If the simple Interest is $2646, then the time = ¹/₃₇₈ × 2646 years

= ^{1 × 2646}/₃₇₈ years

= ²⁶⁴⁶/₃₇₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.

(5) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 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 $7380 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?

(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.

(10) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?