Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $7335

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 = $7335 – $4500 = $2835

Thus, Simple Interest = $2835

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 × 2835}/_{4500 × 9}

= ²⁸³⁵⁰⁰/₄₀₅₀₀

= 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) = $4500

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

Simple Interest = $2835 (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 $4500

= ⁹/₁₀₀ × 4500

= ^{9 × 4500}/₁₀₀

= ⁴⁰⁵⁰⁰/₁₀₀ = 405

Thus, simple Interest for 1 year = $405

Now,

∵ If the simple Interest is $405, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₅ years

∴ If the simple Interest is $2835, then the time = ¹/₄₀₅ × 2835 years

= ^{1 × 2835}/₄₀₅ years

= ²⁸³⁵/₄₀₅ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.

(3) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

(4) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?

(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.

(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.

(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.