Question

The equation for the future value of a deposit earning compound interest is equation 3DP%281%2B%20%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D%20" id="TexFormula1" title="V(t)=P(1+ \frac{r}{n} )^{nt} " alt="V(t)=P(1+ \frac{r}{n} )^{nt} " align="absmiddle" class="latex-formula">, where.......
P = the initial deposit

t = years invested

r = rate at which interest is compounded annually

n = number of times the interest is compounded per year

After 10 years, a $2,000-dollar investment compounded annually has grown to $3600. What is the
interest rate to the nearest whole-number percent?

Answer 1

Answer:

Given that:

The equation for the future value of a deposit earning compound interest is equation:

$V(t) = P(1+\frac{r}{n})^{nt}$              .....[1]

where,

P = the initial deposit

t = years invested

r = rate at which interest is compounded annually

.

n = number of times the interest is compounded per year

As per the statement:

After 10 years, a $2,000-dollar investment compounded annually has grown to $3600.

⇒P = $2000 and V(t) = $3600

Substitute in [1] we have;

$3600 = 2000(1+\frac{r}{1})^{10 \cdot 1}$

Divide both sides by 2000 we have;

$1.8 = (1+r)^{10}$

Taking log base 10 both sides we have;

$\log_{10} 1.8 =\log_{10} (1+r)^{10}$

⇒$0.255272505 = 10 \log_{10} 1+r$

Divide both sides by 10 we have;

$0.0255272505 =\log_{10} 1+r$

⇒$10^{0.0255272505} = 1+r$

Simplify":

$1.06= 1+r$

Subtract 1 from both sides we have;

$0.06=r$

or

r = 0.06 = 6%

Therefore, 6%  is the  interest rate to the nearest whole-number percent

Answer 2

P=2000

t=10

r=?

n=1

3600=2000(1+r/1)^(1*10)

r=0.06

r=6%