Simple Interest
Math MCQs

Question :    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.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $7740

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 = $7740 – $4500 = $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}/_{4500 × 8}

= 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) = $4500

Rate of Simple Interest (R) = 8% 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 = 8% of Principal

= 8% of $4500

= ⁸/₁₀₀ × 4500

= ^{8 × 4500}/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) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

(2) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?

(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?

(6) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?

(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.

(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?

(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.