Question

HELP!!!!

Mr. Martin put $5000 into a trust fund on his daughter's 16th birthday. The trust fund pays 9% interest compounded semiannually. What will the trust fund be worth on her 21st birthday? How much interest did the investment earn? How much interest would have been earned if the trust fund was set up with only simple interest?
We need to carefully read through the problem to pick out the information needed to plug into the compound interest formula:
P - principal = $5000
APR - annual percentage rate = 9% = 0.09
n - # compounding periods a year, semi-annually = 2 (twice a year)
Y - # of years; 21-16 = 5 years
Plugging in we get:
Calculator Keystrokes: 5000 x (1 + 0.09 ÷ 2) ^ (2 x 5) =
To calculate the interest earned, we need to take the final amount and subtract the principal:
$7764.85 - $5000 = $2764.85
And finally, to get the simple interest that would have be earned we plug into the simple interest formula:
i = 5000(0.09)(5) = $2250.00
Jesse decides to invest his income tax refund of $2300 in a CD earning 5.5% interest compounded quarterly. How much will the CD be worth in 3 years? How much more would be earned if it was compounded monthly at the same interest rate?
Quarterly: Monthly:
Difference: $2711.58 - $2709.56 = $2.02
Your Turn: In the previous example, what would the CD have been worth if it was compounded semi-annually? Round to the nearest cent and do not enter the $ symbol.

Answer 1

To solve this, we are going to use the compound interest formula:
`A=P(1+ (r)/(n) )^(nt)`
where

`A` is the final amount after
`t` years.

`P` is the initial amount.

`r` is the interest rate in decimal form.

`n` is the number of times the interest is compounded per year.

`t` is the time in years.

We know from our problem that Jesse's decides to invest his income tax refund of $2300, so
`P=2300`. We also know that the number of years is 3, so
`t=3`. Since the interest was compounded semi-annually, it was compounded 2 times per year; therefore,
`n=2`. Now, to convert the interest rate to decimal form, we are going to divide the rate by 100%

`r= (5.5)/(100)`

`r=0.055`
Now that we have all the values we need, lest replace in our formula:

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

`A=2300(1+ (0.055)/(2))^((2)(3))`

`A=2706.57`

We can conclude that the value of the CD after 3 years of yielding an interest of 5.5% compounded semi-annually is 2706.57