Answer:
1. Interest compounded annually = $18,049.74
2. Interest compounded quarterly = $18,493.77
3. Interest compounded Monthly = $18,598.16
4. Interest compounded continuously = $18,651.19
Explanation:
First let me state the formula for compound interest:
The future value of a certain amount which is compounded is the total amount (Principal + interest) on the amount of money, after compound interests have been applied, and this is shown below:
FV = PV ![(1+\frac{r}{n} )^{n*t}](https://tex.z-dn.net/?f=%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bn%2At%7D)
where:
FV = Future value
PV = Present value = $7,000
r = interest rate in decimal = 0.07
n = number of compounding periods per year
t = compounding period in years = 14
For interests compounded continuously, the Future value is given as:
FV = PV × ![e^{r*t}](https://tex.z-dn.net/?f=e%5E%7Br%2At%7D)
where
is a mathematical constant which is = 2.7183
Now to calculate each on the compounding periods one after the other:
1. Interest compounded annually:
here n (number of compounding periods annually) = 1
Therefore,
FV = 7,000 × ![(1+\frac{0.07}{1})^{14}](https://tex.z-dn.net/?f=%281%2B%5Cfrac%7B0.07%7D%7B1%7D%29%5E%7B14%7D)
FV = 7,000 ×
= $18,049.74
2. Interest compounded quarterly:
here, n = 3 ( there are 4 quarters in a year)
FV = 7,000 × ![(1+\frac{0.07}{4} )^{4*14}](https://tex.z-dn.net/?f=%281%2B%5Cfrac%7B0.07%7D%7B4%7D%20%29%5E%7B4%2A14%7D)
FV = 7,000 ×
= $18,493.77
3. Interest compounded Monthly:
here n = 12 ( 12 months in a year)
FV = 7,000 × ![(1+\frac{0.07}{12} )^{12*14}](https://tex.z-dn.net/?f=%281%2B%5Cfrac%7B0.07%7D%7B12%7D%20%29%5E%7B12%2A14%7D)
FV = 7,000 ×
= $18,598.16
4. Interests compounded continuously:
FV = PV × ![e^{0.07 * 14}](https://tex.z-dn.net/?f=e%5E%7B0.07%20%2A%2014%7D)
FV = 7,000 × 2.66446 = $18,651.19