A child invest $20,000 n a bond that pays 8% interest rate compounded semi-annually. How much money will there be in 18 yrs.
(20000*(1+(0.082))^(2*18)=82078.65
Is this correct
No, compounded Semiannually. You have 36 terms, at an interest rate of 4 percent
20000(1+.04)^36
I am confused where did the 36 terms come in at? and the 4% when the rate is 8%
(20000*(1+(0.08/2))^(2*18)
8% per annum compounded semi-annually
---> 4% every half year
so i = .04
number of half-years in 18 years = 36
amount = 20,000( 1.04^36), as Bob had
= $82,078.65
Yes, your calculation seems to be correct. To calculate the final amount in the bond after 18 years with a semi-annual compounding interest rate of 8%, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $20,000, the annual interest rate (r) is 8% (or 0.08 as a decimal), the interest is compounded semi-annually (n = 2), and the number of years (t) is 18.
Replacing the values into the formula:
A = 20000 * (1 + 0.08/2)^(2*18)
A = 20000 * (1.04)^36
A = 20000 * 2.182382087
A ≈ 82078.65
So, after 18 years, there will be approximately $82,078.65 in the bond.