The Notes: A man has $100 and decides to invest it in a bank for 6 years. The bank gives him two choices, annual rate of interest 2%, compounded annually,...

Monday, September 19, 2011

A man has $100 and decides to invest it in a bank for 6 years. The bank gives him two choices, annual rate of interest 2%, compounded annually,...

Since the bank is paying compound interest , we have to use the formula for compound interest for calculating the amount.

The formula is,

$\displaystyle{A}_{{t}}={P}{{\left({1}+\frac{{r}}{{n}}\right)}}^{{{n}{t}}}$

where ,

$\displaystyle{A}_{{t}}$ is the amount at the end of t years of investment

P is the principal

r is the annual rate of interest,

n is the number of compounding periods per year

Case 1

Given P=$100, t= 6 years , n=1 as interest is compounded annually, r=2%

Now plug in the given values in the formula to calculate the amount at the end of 6 years of investment,

So, $\displaystyle{A}_{{6}}={100}{{\left({1}+\frac{{2}}{{100}}\right)}}^{{6}}$

$\displaystyle{A}_{{6}}={100}{{\left({1}+\frac{{1}}{{50}}\right)}}^{{6}}$

$\displaystyle={100}{{\left(\frac{{51}}{{50}}\right)}}^{{6}}$

$\displaystyle={100}{{\left({1.02}\right)}}^{{6}}$

$\displaystyle={112.6162419}$

$\displaystyle\approx{112.62}$

Case 2

Given: P=$100 , r=1.8% , n=4 ( as interest is compounded quarterly ) , t=6 years

Now plug the given values in the formula to calculate the amount at the end of 6 years,

$\displaystyle{A}_{{6}}={100}{{\left({1}+\frac{{1.8}}{{{4}\cdot{100}}}\right)}}^{{{4}\cdot{6}}}$

$\displaystyle={100}{{\left({1.0045}\right)}}^{{24}}$

$\displaystyle={111.3777874}$

$\displaystyle\approx{111.38}$

So the first option is better with annual rate of interest 2% compounded annually, as the amount received after 6 years of investment is more than the second option.

The Notes

Monday, September 19, 2011

A man has $100 and decides to invest it in a bank for 6 years. The bank gives him two choices, annual rate of interest 2%, compounded annually,...

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