Question

Austin is going to invest in an account paying an interest rate of 2.2% compounded daily. How much would Austin need to invest, , for the value of the account to reach $27,000 in 6 years?

Answer 1

Answer:

Principal, P = $23675.90

Step-by-step explanation:

Given the following data;

Interest rate = 2.2 %

Future value = $27000

Time = 6 years

Number of times = 365 days

To find the principal amount, we would use the compound interest formula;

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

Where;

A is the future value.

P is the principal or starting amount.

r is annual interest rate.

n is the number of times the interest is compounded in a year.

t is the number of years for the compound interest.

Substituting into the equation, we have;

$27000 = P*(1 + \frac{0.022}{365})^{365*6}$

$27000 = P*(1 + 0.000060)^{2190}$

$27000 = P*(1.000060)^{2190}$

$27000 = P*(1.1404)$

$P = \frac {27000}{1.1404}$

Principal, P = $23675.90