Question

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A deposit of $800,000 is made in February 25, 2011. By what date the deposit will be worth $1.2M at 12% compounded annually? What would be the answer if interest was compounded daily? (Use 1 year=360 days.) Why does this date come earlier?

Answer 1

The future value of the investment is calculated as follows

FV = Present value ( 1+interest rate)ⁿ

$ 1,200,000 = $ 800,000 ( 1+0.12)ⁿ

( 1+0.12)ⁿ = 1.5

n = 3.58 years

or by September 24, 2014 the deposit would be worth $ 1.2 million

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If the interest was compounded daily

$ 1,200,000 = $ 800,000 [ (1+(0.12/360))^360t  ]

1.00033³⁶⁰ⁿ = 1.5

360n ln 1.00033 = ln 1.5

n = 3.41 years

or on July 23, 2014 the desposit would be equal to $ 1.2 million

This date comes earler because the number of compounding periods is higher.