A person buys a TV worth BDT 3,90,000 with a down payment of 40,000 including Tk. 5000 as first month's installment. How many more installments does he have to pay if his installments had to double after each successive payment?
Answers
After downpayment amount left=350000
here we apply geometric series where common ratio[r]=2 [since double everytime]
350000=〖5000×2〗^n => 60=2^n [find 2^n for which immediate value >60]
Here 2^6=64>60 ;thus the number installment is 6
Given cost price of a TV = 390000.
Given that he bought a TV with a down payment of 40000 including 5000 as 1st months installment.
= > 40000 - 5000
= > 35000.
Therefore, Money left after down payment = 390000 - 35000
= 355000.
Given that his installment had to double after each successive payment.
As u can see, his 1st month's installment = 5000.
His 2nd month's installment = 10000.
3rd month's installment = 20000.
So, his installments vary from 5000,10000,20000,40000....
As u can see, the given series is in the GP.
where a = 5000, r = 10000/5000 = 2.
We know that sum of first n terms in n GP:
Here r > 1, so, we need to apply the below formula:
= > sn = a(r^n - 1)/r - 1
= > 355000 = 5000(2^n - 1)/(2 - 1)
= > 355000/5000 = (2^n - 1)
= > 71 = 2^n - 1
= > 72 = 2^n
= > 72 = 2^n
= > n ~ 6.
Therefore, the number of more installments = 6.
Hope this helps!