Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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

Amount (A) = $8580

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 = $8580 – $5500 = $3080

Thus, Simple Interest = $3080

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 × 3080}/_{5500 × 8}

= ³⁰⁸⁰⁰⁰/₄₄₀₀₀

= 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) = $5500

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

Simple Interest = $3080 (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 $5500

= ⁸/₁₀₀ × 5500

= ^{8 × 5500}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₀ years

∴ If the simple Interest is $3080, then the time = ¹/₄₄₀ × 3080 years

= ^{1 × 3080}/₄₄₀ years

= ³⁰⁸⁰/₄₄₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

(2) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(5) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?

(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?

(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.

(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(10) 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.