I keep getting confused on this stuff.
Alan invests $2500 in a 5 year Government bond paying interest at 3.7% per annum compounded annually. Calculate the value of the bond at maturity (after 5 yrs)
Tn = 2500(0.037)^5-1
= 2500(0.037)^4
= 2500(1.8741*10^-6)
I know the third step is wrong, but I keep getting to the power of.
your growth factor is 1.037 , not .037
remember: 100% + 3.7% = 1 + .037 = 1.037
2500(1.037)^5 = 2998.01
now = 2500
after year 1 = 2500(1.037)
after year 2 = 2500(1.037)^2
..
after year 5 = 2500(1.037)^5
Don't just rely on "formulas", often it is better to see the pattern and continue in that pattern
To calculate the value of the bond at maturity, follow the steps below:
Step 1: Determine the annual interest rate in decimal form
Given that the interest rate is 3.7% per annum, you need to convert it to a decimal by dividing it by 100.
3.7% = 3.7/100 = 0.037
Step 2: Calculate the compound interest earned per year
Since the bond is compounded annually, you will need to raise (1 + the interest rate) to the power of the number of years.
Compound interest formula: A = P(1 + r)^n
Where:
A = Final amount
P = Principal amount invested (in this case, $2500)
r = Annual interest rate (0.037)
n = Number of years (5 years)
Applying the formula:
A = 2500(1 + 0.037)^5
Step 3: Evaluate the expression
Using a calculator or an appropriate math software, simplify the expression to find the value of the bond at maturity.
A = 2500(1.037)^5
A ≈ 2500(1.207)
So the value of the bond at maturity is approximately $3017.50.
Note: It seems like there was an error in your calculation in Step 2. Instead of using powers, use brackets to raise the number to the power of 5.