Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 7% 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  8

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 7% 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 × 7}

= ³⁰⁸⁰⁰⁰/₃₈₅₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 7% 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 = 7% of Principal

= 7% of $5500

= ⁷/₁₀₀ × 5500

= ^{7 × 5500}/₁₀₀

= ³⁸⁵⁰⁰/₁₀₀ = 385

Thus, simple Interest for 1 year = $385

Now,

∵ If the simple Interest is $385, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₅ years

∴ If the simple Interest is $3080, then the time = ¹/₃₈₅ × 3080 years

= ^{1 × 3080}/₃₈₅ years

= ³⁰⁸⁰/₃₈₅ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.

(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.

(7) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.

(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(9) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.