Question

I need help with this question

Answer 1

3038.28

Explanation:

The formula for accrued amount (principal + interest) when compounded continuously is given by

`A = Pe^(rt)`

where
A is the accrued amount
P is the amount invested
r = annual interest rate as a decimal
t = time in years
e = exponential constant ≈ 2.71828

Therefore

`P = (A)/(e^(rt))`

We are given
A = $9500
r = 9.5% = 0.095 in decimal
t = 12 years

Therefore

`P = (9500)/(e^(0.095 ( 12)))`

`P = (9500)/(e^(1.14))`

`P = (9500)/(3.126768)\\\\P = 3038.28`

So they should invest $3,038.28 now in order to be able to get $9500 in 12 years at annual interest rate of 9.5% if compounded continuously