Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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

Amount (A) = $8470

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 = $8470 – $5500 = $2970

Thus, Simple Interest = $2970

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 × 2970}/_{5500 × 6}

= ²⁹⁷⁰⁰⁰/₃₃₀₀₀

= 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) = $5500

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

Simple Interest = $2970 (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 $5500

= ⁶/₁₀₀ × 5500

= ^{6 × 5500}/₁₀₀

= ³³⁰⁰⁰/₁₀₀ = 330

Thus, simple Interest for 1 year = $330

Now,

∵ If the simple Interest is $330, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₀ years

∴ If the simple Interest is $2970, then the time = ¹/₃₃₀ × 2970 years

= ^{1 × 2970}/₃₃₀ years

= ²⁹⁷⁰/₃₃₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(2) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.

(3) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.

(4) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

(5) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(7) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

(8) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.