Calculate the amount that must be invested at 3.5%p.a.interest compound annually to earn K10000 at the end of 6 years ?

To calculate the amount that must be invested at 3.5% p.a. interest compounded annually to earn K10000 at the end of 6 years, we can use the formula for compound interest:

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

Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (the initial amount of money)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

In this case, we want to find the principal amount (P) that must be invested to earn K10000 at the end of 6 years, with an annual interest rate of 3.5% and interest compounded annually.

A = K10000
r = 0.035
n = 1
t = 6

K10000 = P(1 + 0.035/1)^(1*6)
K10000 = P(1 + 0.035)^6
K10000 = P(1.035)^6
K10000 = P(1.222)
P = K10000 / 1.222
P = K8177.92

Therefore, the amount that must be invested at 3.5% p.a. interest compounded annually to earn K10000 at the end of 6 years is approximately K8177.92.

Formula:

P = A / (1 + r)^n

where:
- P = Principal (amount invested)
- A = Amount (future value)
- r = Interest rate (as a decimal)
- n = Number of years

Given:

- A = K10,000
- r = 3.5% p.a. = 0.035
- n = 6 years

Solution:

P = K10,000 / (1 + 0.035)^6
P = K10,000 / (1.035)^6
P = K10,000 / 1.22987
P = K8,129.56

Therefore, the amount that must be invested at 3.5% p.a. interest compounded annually to earn K10,000 at the end of 6 years is K8,129.56.