Question

How much would you need to deposit in an account…

Answer 1

The rule of the compounded interest is

`A=P(1+(r)/(n))^(nt)`

A is the new amount

P is the initial amount

r is the rate in decimal

n is the number of the period per year

t is the time in years

Since the new amount is $5000, then

A = 5000

Since the time is 10 years, then

t = 10

Since the interest is 6% compounded monthly, then

n = 12

r = 6/100 = 0.06

Substitute them in the rule to find P

`\begin{gathered} 5000=P(1+(0.06)/(12))^((12)(10)) \\ 5000=P(1.005)^(120) \end{gathered}`

Divide both sides by (1.005)^120 to find P

`\begin{gathered} (5000)/((1.005)^(120))=P \\ P=2748.163667 \end{gathered}`

We need to deposit $2748.16 to the nearest hundredth