Question

How much is accumulated over two years in each of the following savings plans ?

a) 40$ at the end of each month for 24 months at 12 percent compounded monthly.

b) 30$ at the end of the first month, 31$ at the end of the second month, and so forth, increasing by 1$ per month at 12 percent compounded monthly.

Answer 1

(A)As per the information provided in the question

Deposits at the end of each month (A) = $40

Period (N) = 24 months

Nominal interest (r) = 12% compounded monthly

Rate of interest per month (i) = 12/12 = 1%

The accumulated deposits = A(F/A,i,N)

The accumulated deposits = 40(F/A,1%,24)

The accumulated deposits = 40(26.9735) = $1078.94

The accumulated deposits in the saving account at the end of 24^th month is $1078.94

(B)As per the information provided in the question

Deposits at the end of first month (A1) = $30

The deposits increases every month (G) = $1

Nominal interest (r) = 12% compounded monthly

Rate of interest per month (i) = 12/12 = 1%

Period (N) = 24 months

Equal deposits in each month (A) = ?

A= A1 + G(A/G,i,N)

A= 30 + 1(A/G,1%,24)

A= 30 + 1(11.0237) = $41.0237

The accumulated deposits = A(F/A,i,N)

The accumulated deposits = 41.0237(F/A,1%,24)

The accumulated deposits = 41.0237(26.9735) = $1106.55

The accumulated deposits in the saving account at the end of 24^th month is $1106.55