Exercise 1: Teacher Kaye is saving P2,000 every month by depositing it in
a bank that gives an interest of 1% compounded quarterly. How much will
she save in 5 years?
Answers
Given : Teacher Kaye is saving P2,000 every month by depositing it in
a bank that gives an interest of 1% compounded quarterly.
To Find : How much will she save in 5 years
Solution:
5 Years has 20 Quarters
Lets break this into Quarters
Amount deposited in 1 Quarter
= 2000 + 2000 + 2000 = 6000
Interest earned = 2000 * 1 * (3/12) /100 + 2000 * 1 * (2/12) /100 + 2000 * 1 * (3/12) /100 = 20 * (3 + 2 + 1) /12 = Rs 10
Amount after 1 Quarter = 6010
Now left 19 Quarters after 1st Quarter
interest rate per Quarter = 1/4 %
1 Qtr deposit becomes = 6010 ( 1 + 1/400)¹⁹
2 Qtr deposit becomes = 6010 ( 1 + 1/400)¹⁸
19th Qtr deposit becomes = 6010 ( 1 + 1/400)¹
20 th Qtr deposit becomes = 6010 ( 1 + 1/400)⁰
1 + 1/400 = 401/400 = 1.0025
Hence total amount after 5 years
6010 + 6010(1.0025) + 6010(1.0025)² + .... + ... + 6010 (1.0025)¹⁸ + 6010 (1.0025)¹⁹
a = 6010
r = 1.0025
n = 20
Sₙ = a(rⁿ - 1)(r - 1)
= 6010 (1.0025²⁰ - 1)/(1.0025 - 1)
= 1,23,098
she save in 5 years = 1,23,098
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Answer:
Step-by-step explanation:
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