Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 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) = 7% per annum

Amount (A) = $6683

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 = $6683 – $4100 = $2583

Thus, Simple Interest = $2583

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 × 2583}/_{4100 × 7}

= ²⁵⁸³⁰⁰/₂₈₇₀₀

= 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) = 7% per annum

Simple Interest = $2583 (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 $4100

= ⁷/₁₀₀ × 4100

= ^{7 × 4100}/₁₀₀

= ²⁸⁷⁰⁰/₁₀₀ = 287

Thus, simple Interest for 1 year = $287

Now,

∵ If the simple Interest is $287, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₇ years

∴ If the simple Interest is $2583, then the time = ¹/₂₈₇ × 2583 years

= ^{1 × 2583}/₂₈₇ years

= ²⁵⁸³/₂₈₇ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.

(3) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

(4) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?

(6) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(8) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?

(9) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.

(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?