Nasir wants to accumulate $1500000 after 10 years. If investment earns interest at the rate of 8 percent per year compounded quarterly, then the amount he must be deposited at the end of each year is
Answers
Given : Nasir wants to accumulate $1500000 after 10 years
investment earns interest at the rate of 8 percent per year compounded quarterly
To find : the amount he must be deposited at the end of each year
Solution :
R = 8 % per annum => 2% per Quarter
1 Year = 4 Quarters
Amounted Deposited at end of each year = P
Amount deposited at end of 10th year = P
Amount deposited at end of 9th year = P(1 + 2/100)⁴
Amount deposited at end of 8th year = P(1 + 2/100)⁸
Amount deposited at end of 1st year = P(1 + 2/100)³⁶
Total Amount
= P + P(1 + 2/100)⁴ + P(1 + 2/100)⁸ + . + . + . + . P(1 + 2/100)³⁶
This is GP
a = P
r = (1 + 2/100)⁴ = (1.02)⁴
n = 10
Sum = P (( 1.02)⁴)¹⁰ - 1)/(1.02⁴ - 1)
1500000 = P (( 1.02)⁴)¹⁰ - 1)/(1.02⁴ - 1)
=> P = 1,02,354.5
the amount he must be deposited at the end of each year is 1,02,354.5 $
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