Question

calculate the number of months it takes for $20,000 to grow by $3600 if money earns 3.6%p.a compounding quarterly

Answer 1

Principal amount =$ 20000

Growth in Amount = $ 3600

Future Value = Amount invested+ Growth amount

= $ 20000+$ 3600

= $ 23600

Interest = 3.6% p.a Compounded Quarterly

We know that Future Value = Present Value ( 1+i/4)^n when interest is compounded Quarterly

Here I = Interest rate

n = No.of Compounding periods

$ 23600= $ 20000( 1+0.036/4)^n

$ 23600= $ 20000( 1+0.009)^n

$ 23600= $ 20000( 1.009)^n

$ 23600/$ 20000 = 1.009^n

1.18 = 1.009^n

Applying log10 on Both sides

Log10 1.18 = Log10 1.009^n

Log10 1.18 = n log10 1.009 [ log m^n = n log m]

0.071882 = n 0.003891

0.071882/0.003891= n

n = 18.47391

No.of Quarterly payments is 18.47391

Each Quarter Comprising of 3 Months

No.of months = 18.47391*3 = 55.42173

Hence Approximately it will take 55 months(Rouding off decimals) to grow $ 20000 by $ 3600.

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