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

Answer:

Lucy needs to invest $55,194.16

Step-by-step 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

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

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;

$\ 84,000 = P \times \left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}$

$P = \dfrac{\ 84,000}{\left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}} =\dfrac{\ 84,000}{1.522} = \ 55,194.16$

Therefore, Lucy needs to invest $55,194.16.