Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 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) = 9% per annum

Amount (A) = $9460

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 = $9460 – $5500 = $3960

Thus, Simple Interest = $3960

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 × 3960}/_{5500 × 9}

= ³⁹⁶⁰⁰⁰/₄₉₅₀₀

= 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) = 9% per annum

Simple Interest = $3960 (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 $5500

= ⁹/₁₀₀ × 5500

= ^{9 × 5500}/₁₀₀

= ⁴⁹⁵⁰⁰/₁₀₀ = 495

Thus, simple Interest for 1 year = $495

Now,

∵ If the simple Interest is $495, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₅ years

∴ If the simple Interest is $3960, then the time = ¹/₄₉₅ × 3960 years

= ^{1 × 3960}/₄₉₅ years

= ³⁹⁶⁰/₄₉₅ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.

(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?

(6) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.

(7) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?

(8) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.

(9) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(10) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.