Question

If $ 8,000 is deposited into an account that pays 12% compounded monthly for 48 months ...

to.

How much money will be in the account after the time of the investment?

b. How much is the return on investment?

C. If, after 48 months, you want to get $ 20,000, how much money should you deposit in an account with the same conditions? That is, 12% compounded monthly.

Answer 1

a.

Formula for compound interest,

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

A = Amount of money accumulated after year n

P = Principal amount = $ 8,000

r = Annual rate of return = 12 % or 0.12

n = Annual compounding frequency = 12

t = Number of years amount is deposited = 4

Substituting all the values on above formula, we get A as:

A = $ 8,000 x (1+0.12/12)⁴⁸

     = $ 8,000 x (1+0.01)⁴⁸

     = $ 8,000 x (1.01)⁴⁸

    = $ 8,000 x 1.61222607768247

    = $ 12,897.8086214597 or $ 12,897.81

After 48 months, there will be $ 12,897.81 in the accounts.

b.

Return on investment = Total accumulated amount – Principal amount

                                  = $ 12,897.81 - $ 8,000 = $ 4,897.81

c.

Principal amount of deposit can be computed using formula for compound interest as:

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

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

    = $ 20,000/ (1+0.01)⁴⁸

   = $ 20,000/ (1.01)⁴⁸

    = $ 20,000/ 1.61222607768247

     = $ 12,405.2081013039 or $ 12,405.21

We need to deposit $ 12,405.21 to get $ 20,000 after 48 months.