Suppose that you have 30000 to invest Determine the total am

Suppose that you have $30,000 to invest. Determine the total amount in the account at end of 10 years for the following options

1. Simple Interest of 5%

2. Interest of 5% compounded monthly (Hint: don\'t round on intermediate steps but round final answer to nearest cent)

3. Interest of 5% compounded continuously (Hint: don\'t round on intermediate steps but round final answer to nearest cent)

Solution

Given that

Invested amount = $30,000

Time = 10 years

1 )

Simple interest rate = 5%

I = PTR / 100

i.e Simple interest I = ( Invested amount x time x rate ) / 100

I = ( $30,000 x 10 x 5 ) / 100

I = $15,00,000 / 100

I = $15000

Total amount in the account at end of 10 years = invested amount + simple interest

= $30,000 + $15000

= $45000

2 ) Rate of interest r = 5 % = 0.05

Total amount in the account at end of 10 years compounded monthly A = P (1 + r/n) ^ nt

Where

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested

p = $30,000 , n = 12, t = 10 years ,r = 5 %

  A = P (1 + r/n) ^ nt

= $30,000 ( 1+0.005/12 )12x10

= $30,000 ( 1.0004 )120

= $30,000 x 1.0491

= $31473

Therefore,

Total amount in the account at end of 10 years compounded monthly = $31473

3 ) Total amount in the account at end of 10 years compounded continuously A = Pe ^rt

where,

P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)

t = number of years

   p = $30000, r = 5% = 0.05 , t = 10 years

   Then

   A = Pe ^rt

= $30,000 x e ^0.05x10

= $30,000 x e ^0.5

   = $30,000 x 1.6487

   = $49461

Therefore,

Total amount in the account at end of 10 years compounded continuously = $49461