4. At the end of every year for 3 years, RM1000 will be invested in an account that offers 8% compounded annualy.Find the account amount at the end of the 3 years.
for annual deposits, just work it out. At the end of year
1: 1000
2: 1000*1.08 + 1000
3: 1000*1.08^2 + 1000*1.08 + 1000
...
n: 1000(1.08^(n-1) + ... + 1)
= 1000(1.08^n - 1)/(1.08-1)
or, for an interest rate of r, the balance at the end of n years is
1000((1+r)^n - 1)/(r)
To find the account amount at the end of 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the account amount at the end of the time period
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount P is RM1000, the annual interest rate r is 8% (or 0.08 in decimal form), the interest is compounded annually (n = 1), and the time period t is 3 years.
Plugging in these values into the formula, we get:
A = 1000(1 + 0.08/1)^(1*3)
A = 1000(1 + 0.08)^3
A = 1000(1.08)^3
A ≈ 1000(1.2597) [rounding to 4 decimal places]
A ≈ RM1259.70
Therefore, the account amount at the end of 3 years would be approximately RM1259.70.
1.08^3 = 1.2597
1.25971 * 1000 = 1,259.71