If 7000 dollars is invested in a bank account at an interest rate of 7 per cent per year, Find the amount in the bank after 14 years if interest is compounded annually: Find the amount in the bank after 14 years if interest is compounded quarterly: Find the amount in the bank after 14 years if interest is compounded monthly: $18598.16$ Finally, find the amount in the bank after 14 years if interest is compounded continuously:

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 [tex](1+\frac{r}{n} )^{n*t}[/tex]

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 × [tex]e^{r*t}[/tex]

where

[tex]e[/tex] 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 × [tex](1+\frac{0.07}{1})^{14}[/tex]

FV = 7,000 × [tex]1.07^{14}[/tex] = $18,049.74

2. Interest compounded quarterly:

here, n = 3 ( there are 4 quarters in a year)

FV = 7,000 × [tex](1+\frac{0.07}{4} )^{4*14}[/tex]

FV = 7,000 × [tex]1.0175^{56}[/tex] = $18,493.77

3. Interest compounded Monthly:

here n = 12 ( 12 months in a year)

FV = 7,000 × [tex](1+\frac{0.07}{12} )^{12*14}[/tex]

FV = 7,000 × [tex]1.005833^{168}[/tex] = $18,598.16

4. Interests compounded continuously:

FV = PV × [tex]e^{0.07 * 14}[/tex]

FV = 7,000 × 2.66446 = $18,651.19