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) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?

(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.

(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?

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

(9) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.