Answered

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How much would you need to deposit in an account now in order to have $5000 in the account in 5 years? Assume the account earns 5% interest compounded daily.

Sagot :

Answer:

$3893.97

Step-by-step explanation:

5000 = x (1 + 0.05/365)^365 * 5

5000 = x ( 1 + 0.000137)^1825

5000 =  x (1.000137)^1825

5000 = 1.284036 x

1.284036 / 1.284036 x = 5000 / 1.284036

x = 3 893.97182

x = 3 893.97

semsee45

Answer:

$3,894.07

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

  • A = $5,000
  • r = 5% = 0.05
  • n = 365 (daily)
  • t = 5 years

Substitute the given values into the formula and solve for P:

[tex]\implies 5000=P\left(1+\dfrac{0.05}{365}\right)^{365 \times 5}[/tex]

[tex]\implies 5000=P\left(1.000136986...\right)^{1825}[/tex]

[tex]\implies P=\dfrac{5000}{\left(1.000136986...\right)^{1825}}[/tex]

[tex]\implies P=3894.070588...[/tex]

Therefore, the amount you would need to deposit in an account now in order to have $5,000 in the account in 5 years time is $3,894.07.

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