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 $7052 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) = 8% per annum

Amount (A) = $7052

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 = $7052 – $4300 = $2752

Thus, Simple Interest = $2752

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 × 2752}/_{4300 × 8}

= ²⁷⁵²⁰⁰/₃₄₄₀₀

= 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) = 8% per annum

Simple Interest = $2752 (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 $2752, then the time = ¹/₃₄₄ × 2752 years

= ^{1 × 2752}/₃₄₄ years

= ²⁷⁵²/₃₄₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(2) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

(5) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.

(8) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?

(9) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.

(10) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.