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:

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

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 ×

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 ×

FV = 7,000 × = $18,049.74

2. Interest compounded quarterly:

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

FV = 7,000 ×

FV = 7,000 × = $18,493.77

3. Interest compounded Monthly:

here n = 12 ( 12 months in a year)

FV = 7,000 ×

FV = 7,000 × = $18,598.16

4. Interests compounded continuously:

FV = PV ×

FV = 7,000 × 2.66446 = $18,651.19

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