Question

Lucy is going to invest in an account paying an interest rate of 7% compounded daily. How much would Lucy need to invest, to the nearest dollar, for the value of the account to reach $84,000 in 6 years?

Answer 1

Lucy needs to invest $55,194.16

Explanation:

The given information are;

The interest rate of the account = 7% compounded daily

The amount at the end of 6 years = $84,000

The time duration = 6 years

The amount Lucy

The formula for compound interest is

`A(t) = P * \left ( 1 + (r)/(n) \right )^(n * t)`

Where;

r = The interest rate = 7% = 0.07

n = The number of times a year = 365

t = The number years = 6 years

A(t) = The amount after 6 years = $84,000

P = The initial amount invested

Therefore, we have;

`\$ 84,000 = P * \left ( 1 + (0.07)/(365) \right )^(365 * 6)`

`P = (\$84,000)/(\left ( 1 + (0.07)/(365) \right )^(365 * 6)) =(\$84,000)/(1.522) = \$55,194.16`

Therefore, Lucy needs to invest $55,194.16.