Question

Find the balance and interest of $4200 deposited at 2.7% for 5 years.Calculate the values using quarterly compounding.Balance = _________Interest = __________ Calculate the values using annual compounding.Balance = _________Interest = __________Calculate the values using simple interest.Balance = _________Interest = _________

Answer 1

`\begin{gathered} a)\text{ Balance = \$4804.87} \\ \text{Interest = \$604.87} \\ \\ b)\text{Balance = \$}4798.46 \\ \text{Interest = \$}598.46 \\ \\ c)\text{ Balance = \$4767} \\ Interest\text{ = \$567} \end{gathered}`Step-by-step explanation:

a) Principal = $4200

rate = 2.7% = 0.027

time = 5 years

Balance = ?

n = 4 (quarterly)

Using compund interest formula:

`FV\text{ = P(1 +}(r)/(n))^(nt)`
`\begin{gathered} FV\text{ = balance} \\ \text{Balance = 4200(1 + }(0.027)/(4))^(4*5) \\ \text{Balance = 4200(1 + }0.00675)^(20) \\ \text{Balance = 4804.87} \\ \\ \text{Interest = Balance - principal} \\ \text{Interest = \$4804.87 - \$4200} \\ \text{Interest = \$604.87} \end{gathered}`

For annual compounding, n = 1

`\begin{gathered} FV\text{ = balance} \\ \text{Balance = 4200(1 + }(0.027)/(1))^(1*5) \\ \text{Balance = 4200(1 + }0.027)^5 \\ \text{Balance = \$ }4798.46 \\ \\ \text{Interest = Balance - principal} \\ \text{Interest = \$}4798.46\text{ - \$4200} \\ \text{Interest = \$}598.46 \end{gathered}`

Using simple interest:

`\begin{gathered} I\text{ = PRT} \\ I\text{ = interest, P = principal, R = rate, T = time} \\ I\text{ = }4200*0.027*5 \\ Interest\text{ = \$567} \\ \\ \text{Balance = Principal + Interest} \\ \text{Balance = 4200 + 567} \\ \text{Balance = \$4767} \end{gathered}`