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Priyanka has a recurring deposit account of Rs 1000 per month at 10% per annum . If she gets Rs 5550 as interest at the time of maturity find the total time for which the account is held? |
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Answer» Answer: Step-by-step explanation: Let the MATURITY PERIOD be n months, P be the money DEPOSITED every month which is Rs.1000 and r be the rate of interest per annum which is 10%. Now, the interest I received at the END of maturity is calculated by the FOLLOWING formula: I=P× 24 n(n+1) × 100 r
We are given I=5500, so substituting the values, we get ⇒5550=1000× 24 n(n+1) × 100 10
⇒n(n+1)= 100 5550×24 =1332 ⇒n 2 +n−1332=0 ⇒n 2 +37n−36n−1332=0 ⇒(n−36)(n+37)=0 ⇒n=36, −37 Since the maturity period cannot be negative, n=36. Therefore, the total time for which the account was held was 36 months which is the same as 3 years. So the maturity period was 3 years.Let the maturity period be n months, P be the money deposited every month which is Rs.1000 and r be the rate of interest per annum which is 10%. Now, the interest I received at the end of maturity is calculated by the following formula: I=P× 24 n(n+1) × 100 r
We are given I=5500, so substituting the values, we get ⇒5550=1000× 24 n(n+1) × 100 10
⇒n(n+1)= 100 5550×24 =1332 ⇒n 2 +n−1332=0 ⇒n 2 +37n−36n−1332=0 ⇒(n−36)(n+37)=0 ⇒n=36, −37 Since the maturity period cannot be negative, n=36. Therefore, the total time for which the account was held was 36 months which is the same as 3 years. So the maturity period was 3 years. |
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