Simple Interest
Math MCQs

Question :    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.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $10212

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 = $10212 – $6900 = $3312

Thus, Simple Interest = $3312

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 × 3312}/_{6900 × 8}

= ³³¹²⁰⁰/₅₅₂₀₀

= 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) = $6900

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

Simple Interest = $3312 (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 $6900

= ⁸/₁₀₀ × 6900

= ^{8 × 6900}/₁₀₀

= ⁵⁵²⁰⁰/₁₀₀ = 552

Thus, simple Interest for 1 year = $552

Now,

∵ If the simple Interest is $552, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₂ years

∴ If the simple Interest is $3312, then the time = ¹/₅₅₂ × 3312 years

= ^{1 × 3312}/₅₅₂ years

= ³³¹²/₅₅₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(2) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(3) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.

(4) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.

(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?