Question

if 3000 dollars is invested in a bank account at an interest rate of 6 percent per year find the amount in the bank after 10 years if interest is compounded quarterly

Answer 1

if 3000 dollars is invested in a bank account at an interest rate of 6 percent per year find the amount in the bank after 10 years if interest is compounded quarterly ​

we know that

The compound interest formula is equal to

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

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=3,000

r=6%=6/100=0.06

t=10 years

n=4

substtute in the formula above

`\begin{gathered} A=3,000(1+(0.06)/(4))^(4\cdot10) \\ \\ A=3,000((4.06)/(4))^(40) \\ \\ A=\$5,442.06 \end{gathered}`

Part 2

compounded monthly

we have

P=3,000

r=6%=6/100=0.06

t=10 years

n=12

substtute in the formula above

`\begin{gathered} A=3,000(1+(0.06)/(12))^(12\cdot10) \\ \\ A=3,000((12.06)/(12))^(120) \\ \\ A=\$5,458.19 \end{gathered}`

Part 3

continuously

we know that

The formula to calculate continuously compounded interest is equal to

`A=P(e)^(rt)`

`A=P\mleft(e\mright)^{\mleft\{rt\mright\}}`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

P=3,000

r=6%=6/100=0.06

t=10 years

substitute

`\begin{gathered} A=3,000(e)^{\{0.06\cdot10\}} \\ A=\$5,466.36 \end{gathered}`