Question

a stock broker allocated $100,000 to an account earning 4% per year compounded continuously. if no withdrawals are made, how much was in the account at the end of four years? round the answer to nearest dollar.

Answer 1

$100,000 was allocated by a stockbroker to a portfolio yielding 4% annually compounded. If no withdrawals are taken, there will be $117,352 left in the account after four years.

Given a certain rate of return, present value (PV) is the current value of a future financial asset or stream of cash flows. A discount rate or the interest rate that could be obtained through investment is applied to the future value to get the present value.

According to the continuously compounded interest formula,

FV = PV $e^{it}$

Here,

Present Investment Value, or PV

the interest rate, I

T = time in years

So,

In light of the specified

PV = $ 100,000

I = 4% = 0.04

t = 4 years

Hence

FV stands for "Final Investment Value"

Then,

FV = 100,000 * e⁰.⁰⁴ˣ⁴

FV = 100,000*e⁰.¹⁶

FV = 100,000 * 1.173510871

FV = 117351.0871

FV = 117351

Hence

The balance in the account after four years was = $117,352

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