Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $7310

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 = $7310 – $4300 = $3010

Thus, Simple Interest = $3010

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 × 3010}/_{4300 × 10}

= ³⁰¹⁰⁰⁰/₄₃₀₀₀

= 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) = $4300

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3010 (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 = 10% of Principal

= 10% of $4300

= ¹⁰/₁₀₀ × 4300

= ^{10 × 4300}/₁₀₀

= ⁴³⁰⁰⁰/₁₀₀ = 430

Thus, simple Interest for 1 year = $430

Now,

∵ If the simple Interest is $430, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₀ years

∴ If the simple Interest is $3010, then the time = ¹/₄₃₀ × 3010 years

= ^{1 × 3010}/₄₃₀ years

= ³⁰¹⁰/₄₃₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?

(2) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(4) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(5) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.

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

(8) 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.

(9) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?