Question

Mr. Mike has a savings account with first deposit of $1200 and afterwards deposits $56 a week. Compute the value of the account at time t > 0 assuming the bank pays 8% interest compounded without a pause.

Answer 1

Initial deposit = $1200

Bank interest rate = 8%

I year = 52 weeks.

Amount of savings per week = $\$$ 56

Deposit amounts per year = $\$56*52 = \$2912$

Value at time t>0 = $\$2912/0.08 = \$36,400$

Total Value = Initial deposit + value at time>0

Value = $\$36,400 + \$1200$

Value = $ 37,600

Explanation

At any point in time above time 0 (t>0), the value of the weekly deposit is equal to to ($2912 per year) will be equivalent to amounts received in perpetuity. The amount in this case will be equal to the value of the yearly deposits ($2912) divided by the bank interest rate of 8%(0.08). The total value is equal to the amount in perpetuity plus the initial deposit of $1200 which results to a total value of $37600.