Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5200

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

Amount (A) = $8476

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 = $8476 – $5200 = $3276

Thus, Simple Interest = $3276

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 × 3276}/_{5200 × 7}

= ³²⁷⁶⁰⁰/₃₆₄₀₀

= 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) = $5200

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

Simple Interest = $3276 (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 $5200

= ⁷/₁₀₀ × 5200

= ^{7 × 5200}/₁₀₀

= ³⁶⁴⁰⁰/₁₀₀ = 364

Thus, simple Interest for 1 year = $364

Now,

∵ If the simple Interest is $364, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₄ years

∴ If the simple Interest is $3276, then the time = ¹/₃₆₄ × 3276 years

= ^{1 × 3276}/₃₆₄ years

= ³²⁷⁶/₃₆₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(2) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(4) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.

(8) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(9) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?

(10) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.