Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7224

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 = $7224 – $4200 = $3024

Thus, Simple Interest = $3024

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 × 3024}/_{4200 × 8}

= ³⁰²⁴⁰⁰/₃₃₆₀₀

= 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) = $4200

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3024 (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 $4200

= ⁸/₁₀₀ × 4200

= ^{8 × 4200}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $3024, then the time = ¹/₃₃₆ × 3024 years

= ^{1 × 3024}/₃₃₆ years

= ³⁰²⁴/₃₃₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.

(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?

(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(6) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.

(9) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.