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 $7396 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $7396

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 = $7396 – $4300 = $3096

Thus, Simple Interest = $3096

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 × 3096}/_{4300 × 9}

= ³⁰⁹⁶⁰⁰/₃₈₇₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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 = $3096 (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 $3096, then the time = ¹/₃₈₇ × 3096 years

= ^{1 × 3096}/₃₈₇ years

= ³⁰⁹⁶/₃₈₇ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.

(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?

(9) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.