Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $10132

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 = $10132 – $6800 = $3332

Thus, Simple Interest = $3332

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 × 3332}/_{6800 × 7}

= ³³³²⁰⁰/₄₇₆₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6800

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3332 (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 = 7% of Principal

= 7% of $6800

= ⁷/₁₀₀ × 6800

= ^{7 × 6800}/₁₀₀

= ⁴⁷⁶⁰⁰/₁₀₀ = 476

Thus, simple Interest for 1 year = $476

Now,

∵ If the simple Interest is $476, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₆ years

∴ If the simple Interest is $3332, then the time = ¹/₄₇₆ × 3332 years

= ^{1 × 3332}/₄₇₆ years

= ³³³²/₄₇₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.

(3) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?

(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(6) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.

(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.

(8) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.