Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 8% 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  9

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 8% 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 × 8}

= ³⁰⁹⁶⁰⁰/₃₄₄₀₀

= 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) = 8% 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 = 8% of Principal

= 8% of $4300

= ⁸/₁₀₀ × 4300

= ^{8 × 4300}/₁₀₀

= ³⁴⁴⁰⁰/₁₀₀ = 344

Thus, simple Interest for 1 year = $344

Now,

∵ If the simple Interest is $344, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₄ years

∴ If the simple Interest is $3096, then the time = ¹/₃₄₄ × 3096 years

= ^{1 × 3096}/₃₄₄ years

= ³⁰⁹⁶/₃₄₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?

(2) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.

(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?

(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.

(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.

(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(10) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.