Hari decides to save * 1,800 by making payments
at the end of each month for two years in a
security, paying interest at the rate of 4% p.a.
converted monthly. How much is each of the
payment.
Answers
Given : Hari decides to save * 1,800 by making payments at the end of each month for two years in a security, paying interest at the rate of 4% p.a. converted monthly
To Find : How much is each of the payment
Solution:
Let say He Makes a Payment = P each month
Interest for 1st payment is for 23 months
interest for 2nd payment is for 22 months
interest for last payment (24th) is for for 0 months
Total Payments = 24*P
Considering simple interest
Total interest = P * (4/12) * (23 + 22 + ............................+ 1 + 0) /100
= (P/300)( 23 * 24 / 2)
= 92P/100
24P + 92P/100 = 1800
=> 2400P + 92P = 180000
=> 2492P = 1800000
=> P = 72.23
each of the payment. = 72.23
Considering compound interest
1800 = P * { (1 + 4/1200)²³ + (1 + 4/1200)²² + .............................+ (1 + 4/1200)²⁰}
1800= P { (301/300)²³ + (301/300)²² +...........................+ 1)
1800 = P * ((301/300)²⁴ - 1 ) /(301/300 - 1)
1800 = P * ((301/300)²⁴ - 1 ) /(1/300)
6 = P * (301/300)²⁴ - 1)
=> P = 72.16
each of the payment. = 72.16
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