Compound Interest - Questions
$3000 is invested for 18 months compounded at the interest rate of 0.75% every month. Give answer correct to the nearest cent, wherever necessary.
a. Calculate the final value of this investment
b. What is the increase in value obtained in part (a) as against investing the same amount for same time at same rate but at simple interest.
(a)
$$\begin{aligned}
\text{Pricipal Amount} & =\$3000\\
\text{Compunding Rate of Interest} &= 0.75\%~\text{p.m.}\\
\text{Time Period}&=18~\text{month}\\
\text{Total Amount,}~A &=\$3000 \times 1.0075^{18}\\
&\approx \$3431.88 \end{aligned}$$ (b) $$\begin{aligned}
\text{If same amount is invested for same time} & \text{but at a simple rate..}\\
\text{Amount} A^{\prime} & =\$3000(1+0.0075\times 18)\\
&=\$3405\\
\text{Increase in value obtained}&=\$3431.88-\$3405\\
&=\$26.88
\end{aligned}$$
Calculate the increase in total interest amount earned from year 3 to year 4 on an investment of $10000 at 4% compounded interest p.a. Give answer correct to the nearest dollar, wherever necessary.
\begin{aligned}
\text{Amount of \$10000 after 3 years}&=\$10000\times 1.04^3\\
&=\$11248.64\\
\text{Interest amount earned}&=\$11248.64-\$10000\\
&=\$1248.64\\
\text{Amount of \$10000 after 4 years}&=\$10000 \times 1.04^4\\
&\approx \$11698.59\\
\text{Interest amount earned} & = \$11698.59 - \$10000\\
&=\$ 1698.59\\
\text{Hence from year 3 to year 4,}&\\
\text{Increase in total interest amount earned}&=\$1698.59-\$1248.64\\
&=\$449.95\\
&\approx \$ 450
\end{aligned}
Choose which investment is the best of all in terms of total amount earned. All rates are applied based on compounding method.
$1200 for 5 years at 5.6% p.a.
$1350 for 4 years at 3.3% p.a.
$1100 for 3 years at 10.5% p.a.
$1400 for 2 years at 5% p.a.
How much more interest is earned on \(\$ 50,000\) if interest at \({\rm{8\% p}}{\rm{.a}}{\rm{. }}\) is compounded quarterly over \(5\) years, rather than simple interest of \(8\%\) over the same time?
\(\$ 4297.32\)
\(\$ 4097.32\)
\(\$ 4197.32\)
\(\$ 3997.32\)
\($3,000\) is invested for \(18\) months compounded at the interest rate of \(0.75\%\) every month. Give your answer correct to the nearest cent, wherever necessary.
a. Calculate the final value of this investment
b. What is the increase in value obtained in part (a) as against investing the same amount for same time at same rate but at simple interest.
Samuel likes investing in mutual funds. He invested \($6,000\) in Fund A, \(3\) years ago that earned him \(7.5\%\) annual compounded interest. He also invested \($10,000\) in Fund B, \(2\) years ago that earned him \(9\%\) annual compounded interest. Calculate the following, to the nearest cent
a. What is the total value of Samuel’s investments as of today?
b. Which investment has earned Samuel more interest?
