Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7240

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 = $7240 – $4000 = $3240

Thus, Simple Interest = $3240

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 × 3240}/_{4000 × 9}

= ³²⁴⁰⁰⁰/₃₆₀₀₀

= 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) = $4000

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3240 (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 = 9% of Principal

= 9% of $4000

= ⁹/₁₀₀ × 4000

= ^{9 × 4000}/₁₀₀

= ³⁶⁰⁰⁰/₁₀₀ = 360

Thus, simple Interest for 1 year = $360

Now,

∵ If the simple Interest is $360, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₀ years

∴ If the simple Interest is $3240, then the time = ¹/₃₆₀ × 3240 years

= ^{1 × 3240}/₃₆₀ years

= ³²⁴⁰/₃₆₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.

(2) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.

(4) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?

(5) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.

(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.

(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.