Question

How much money has to be invested at 5.9% interest compounded continuously to have $15,000 after 12 years?

7465.50
7402.26
7427.73
7389.43

Answer 1

The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.

Explanation:

The given is,

Future value, F = $15,000

Interest, i = 5.9%

( compounded continuously )

Period, t = 12 years

Step:1

Formula to calculate the present with compounded continuously,

`F=Pe^((i)(t))`...............(1)

Substitute the values in equation (1) to find the P value,

`15000=Pe^((0.059)(12))` ( ∵
`i = (5.9)/(100)=0.059` )

`15000=Pe^(0.708)`

`15000=P(2.0299)` ( ∵
`e^(o.708) =2.0299` )

We change the P (Present value) into the left side,

`P=(15000)/(2.0299)`

`=7389.427`

≅ 7389.43

P = $ 7389.43

Result:

The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.