Tim wishes to turn her K10,000 investment into K100 000 in 20 years. How much interest does she need to receive compounded annually to reach her goal? ?

To calculate the interest needed to turn K10,000 into K100,000 in 20 years, we can use the compound interest formula:

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

Where:
A = the future value of the investment (K100,000)
P = the principal amount (K10,000)
r = the annual interest rate
n = the number of times the interest is compounded per year
t = the number of years

We need to solve for the annual interest rate (r) in order to determine how much interest Tim needs to receive.

Substitute the given values into the formula:

K100,000 = K10,000(1 + r/1)^(1*20)

Divide both sides by K10,000:

10 = (1 + r)^20

Take the 20th root of both sides:

1.148698355 = 1 + r

Subtract 1 from both sides:

r = 0.148698355 or 14.87%

Therefore, Tim needs to receive an annual interest rate of approximately 14.87% compounded annually in order to turn her K10,000 investment into K100,000 in 20 years.

Step 1: Calculate the future value (FV)

FV = P-(1 + r)^n
where:
- P = present value (initial investment)
- r = annual interest rate
- n = number of years

FV = 10,000-(1 + r)^20 = 100,000

Step 2: Solve for the annual interest rate (r)

100,000 = 10,000-(1 + r)^20
(1 + r)^20 = 100,000/10,000
(1 + r)^20 = 10

Step 3: Take the 20th root of both sides

1 + r = 10^(1/20)
r = 10^(1/20) - 1
r = 0.0630 or 6.30%

Therefore, Tim needs to receive 6.30% interest compounded annually to turn her K10,000 investment into K100,000 in 20 years.