Question

Find the accumulated value of an investment of 15,000 for 4 years at an interest of 4% if the money is a. Compound semiannually; b. Compounded quarterly; c. Compounded monthly; d. Compounded continuously.

Answer 1

Answer:

Compounded Semiannually: $17,574.89

Compounded Quarterly: $17,588.68

Compounded Monthly: $17,597.98

Compounded Continuously: $17,602.66

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

$A=P(1+\frac{r}{n} )^{nt}$

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 4% into a decimal:

4% -> $\frac{4}{100}$ -> 0.04

Now, plug in the values to the equation:

Compounded Semiannually:

$A=15,000(1+\frac{0.04}{2})^{2(4)}$

$A=17,574.89$

Compounded Quarterly:

$A=15,000(1+\frac{0.04}{4})^{4(4)}$

$A=17,588.68$

Compounded Monthly:

$A=15,000(1+\frac{0.04}{12})^{12(4)}$

$A=17,597.98$

To find the value if compounded continuously, use the following formula:

$A = Pe^{rt}$

$A=15,000e^{0.04(4)}$

$A=17,602.66$