Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $7052

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 = $7052 – $4100 = $2952

Thus, Simple Interest = $2952

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 × 2952}/_{4100 × 8}

= ²⁹⁵²⁰⁰/₃₂₈₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4100

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

Simple Interest = $2952 (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 $4100

= ⁸/₁₀₀ × 4100

= ^{8 × 4100}/₁₀₀

= ³²⁸⁰⁰/₁₀₀ = 328

Thus, simple Interest for 1 year = $328

Now,

∵ If the simple Interest is $328, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₈ years

∴ If the simple Interest is $2952, then the time = ¹/₃₂₈ × 2952 years

= ^{1 × 2952}/₃₂₈ years

= ²⁹⁵²/₃₂₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(2) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?

(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(6) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

(7) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?

(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.

(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.