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 $7810 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7810

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 = $7810 – $5500 = $2310

Thus, Simple Interest = $2310

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 × 2310}/_{5500 × 7}

= ²³¹⁰⁰⁰/₃₈₅₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $2310 (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 $2310, then the time = ¹/₃₈₅ × 2310 years

= ^{1 × 2310}/₃₈₅ years

= ²³¹⁰/₃₈₅ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(3) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.

(5) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.

(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?

(8) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?

(9) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?

(10) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.