Question

Celesta wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly in an account if she were to deposit the money today. She needs to have $10,000 in three years. How much will she have to deposit today

Answer 1

Given:

Amount after three years = $10000

Rate of interest = 8.2 percent compounded monthly = 0.082

Time = 3 years

To find:

The principal value.

Solution:

Formula for amount is

$A=P\left(1+\dfrac{r}{n}\right)^{nt}$

where, P is principal, r is rate of interest, n is the number of times interest compounded in an year, t is number of years.

Substitute A=10000, r=0.082, n=12 and t=3 in the above formula.

$10000=P\left(1+\dfrac{0.082}{12}\right)^{12(3)}$

$10000=P\left(1+\dfrac{41}{6000}\right)^{36}$

$10000=P\left(\dfrac{6041}{6000}\right)^{36}$

$10000=P(1.27783)$

Divide both sides by 1.27783.

$\dfrac{10000}{1.27783}=P$

$7825.76712=P$

$P\approx 7825.767$

Therefore, today she have to deposit $7825.767.