Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6468

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 = $6468 – $4200 = $2268

Thus, Simple Interest = $2268

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 × 2268}/_{4200 × 6}

= ²²⁶⁸⁰⁰/₂₅₂₀₀

= 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) = $4200

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2268 (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 = 6% of Principal

= 6% of $4200

= ⁶/₁₀₀ × 4200

= ^{6 × 4200}/₁₀₀

= ²⁵²⁰⁰/₁₀₀ = 252

Thus, simple Interest for 1 year = $252

Now,

∵ If the simple Interest is $252, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₅₂ years

∴ If the simple Interest is $2268, then the time = ¹/₂₅₂ × 2268 years

= ^{1 × 2268}/₂₅₂ years

= ²²⁶⁸/₂₅₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(4) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(5) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?

(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?

(7) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(8) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.

(10) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.