Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7783

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 = $7783 – $4300 = $3483

Thus, Simple Interest = $3483

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 × 3483}/_{4300 × 9}

= ³⁴⁸³⁰⁰/₃₈₇₀₀

= 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) = $4300

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3483 (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 = 9% of Principal

= 9% of $4300

= ⁹/₁₀₀ × 4300

= ^{9 × 4300}/₁₀₀

= ³⁸⁷⁰⁰/₁₀₀ = 387

Thus, simple Interest for 1 year = $387

Now,

∵ If the simple Interest is $387, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₇ years

∴ If the simple Interest is $3483, then the time = ¹/₃₈₇ × 3483 years

= ^{1 × 3483}/₃₈₇ years

= ³⁴⁸³/₃₈₇ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.

(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?

(3) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

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

(6) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(9) Ashley had to pay $4823 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 Mary borrowed a sum of $5050 at a rate of 10% simple interest.