Notes: You have recently decided to invest in a CD. Your CD is paying 2.5% for the next two years. You are investing $2,000 in your CD. How much...

Friday, 30 December 2016

You have recently decided to invest in a CD. Your CD is paying 2.5% for the next two years. You are investing $2,000 in your CD. How much...

Given Principal(P)=$2000, Time period (t)=2 years, Annual Interest Rate=2.5%

Now the amount at the end of two years will depend on, whether the interest is paid as simple interest or compound interest and the compounding periods. This is not stated in the question.

a) Amount on the basis of simple interest

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

$\displaystyle{A}={2000}{\left({1}+\frac{{2.5}}{{100}}\cdot{2}\right)}$

$\displaystyle{A}={2000}{\left({1}+{0.05}\right)}$

$\displaystyle{A}={2100}$

CD will be worth $2100, if simple interest is considered.

b) Assuming compound interest on annual basis

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

$\displaystyle{A}={2000}{{\left({1}+\frac{{2.5}}{{100}}\right)}}^{{2}}$

$\displaystyle{A}={2000}{{\left({1.025}\right)}}^{{2}}$

...

Given Principal(P)=$2000, Time period (t)=2 years, Annual Interest Rate=2.5%

Now the amount at the end of two years will depend on, whether the interest is paid as simple interest or compound interest and the compounding periods. This is not stated in the question.

a) Amount on the basis of simple interest

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

$\displaystyle{A}={2000}{\left({1}+\frac{{2.5}}{{100}}\cdot{2}\right)}$

$\displaystyle{A}={2000}{\left({1}+{0.05}\right)}$

$\displaystyle{A}={2100}$

CD will be worth $2100, if simple interest is considered.

b) Assuming compound interest on annual basis

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

$\displaystyle{A}={2000}{{\left({1}+\frac{{2.5}}{{100}}\right)}}^{{2}}$

$\displaystyle{A}={2000}{{\left({1.025}\right)}}^{{2}}$

$\displaystyle{A}={2101.25}$

CD will yield $2101.25, if compound interest is considered on annual basis.

c) If interest is compounded quarterly

$\displaystyle{A}={P}{{\left({1}+\frac{{2.5}}{{{4}\cdot{100}}}\right)}}^{{{4}\cdot{2}}}$

$\displaystyle{A}={2000}{{\left({1}+{0.00625}\right)}}^{{8}}$

$\displaystyle{A}={2000}{{\left({1.00625}\right)}}^{{8}}$

$\displaystyle{A}={2102.215}$

CD will yield $\displaystyle\approx$ $2102.22, if interest is compounded quarterly.

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