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 $7200 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $7200

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 = $7200 – $4500 = $2700

Thus, Simple Interest = $2700

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 × 2700}/_{4500 × 6}

= ²⁷⁰⁰⁰⁰/₂₇₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $2700 (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 $2700, then the time = ¹/₂₇₀ × 2700 years

= ^{1 × 2700}/₂₇₀ years

= ²⁷⁰⁰/₂₇₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

(2) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(5) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(6) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?

(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(8) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?

(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.

(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.