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

Principal, P = $23675.90

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 + (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 + (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