Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4500

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6390

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 = $6390 – $4500 = $1890

Thus, Simple Interest = $1890

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 × 1890}/_{4500 × 6}

= ¹⁸⁹⁰⁰⁰/₂₇₀₀₀

= 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) = $4500

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1890 (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 = 6% of Principal

= 6% of $4500

= ⁶/₁₀₀ × 4500

= ^{6 × 4500}/₁₀₀

= ²⁷⁰⁰⁰/₁₀₀ = 270

Thus, simple Interest for 1 year = $270

Now,

∵ If the simple Interest is $270, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₇₀ years

∴ If the simple Interest is $1890, then the time = ¹/₂₇₀ × 1890 years

= ^{1 × 1890}/₂₇₀ years

= ¹⁸⁹⁰/₂₇₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?

(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?

(4) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(6) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?

(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.