Question

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:

Answer 1

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 $(1+\frac{r}{n} )^{n*t}$

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 × $e^{r*t}$

where

$e$ 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 × $(1+\frac{0.07}{1})^{14}$

FV = 7,000 × $1.07^{14}$ = $18,049.74

2. Interest compounded quarterly:

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

FV = 7,000 × $(1+\frac{0.07}{4} )^{4*14}$

FV = 7,000 × $1.0175^{56}$ = $18,493.77

3. Interest compounded Monthly:

here n = 12 ( 12 months in a year)

FV = 7,000 × $(1+\frac{0.07}{12} )^{12*14}$

FV = 7,000 × $1.005833^{168}$ = $18,598.16

4. Interests compounded continuously:

FV = PV × $e^{0.07 * 14}$

FV = 7,000 × 2.66446 = $18,651.19