Question

Burt deposits $10,000 into a bank account today. The account earns 5% per annum compounding daily for the first 2 years, then 5.5% per annum compounded quarterly thereafter. No further deposits or withdrawals will be made.

For this question, assume all months are of equal length (30 days) and ignore leap years.

(d) Calculate the account balance 10 years from today.

Answer 1

From the information given in above question we have to find out Account Balance after 10 yeras from today.

Principal amount = $10,000

First two years of interest rate = 5% per annum

(i).

Compounding daily and it is also given that the number of days in month is 30 days over the year, so the number of days in a year will be = 30 * 12 = 360 days and in two years = 360 * 2 = 720 days

Rate of interest daily basis = 5% / 360 = 0.01389% daily basis

Amount in Bank after 2 year = Principal Amount deposited * ( 1 + interest rate on a daily basis)^time period in days

Therefore, Amount after 2 years = $10,000 * ( 1 + 0.01389%)^720 = $11,051.72

(ii).

Now it is given in the question that the interest rate after two years is 5.5% per annum compounded quaterly.

Now, Interest rate per quarter = 5.5% / 4 = 1.375% per quarter

Number of quarter in a year = 4

Number of quarter in 8 years ( 10 - 2 = 8 ) = 8 *4 = 32 quarters.

Now the invested amount has become $11,051.72 after 2 years. so we will consider this amount as a Principal amount for the next 8 years.

Therefore, Amount in Bank after 10 years of deposits = $11,051.72 * ( 1+ 1.375% ) ^ 32 = $17,108.724

Hence, the amount invested in Bank has become $17,108.724 after 10 years given the deposit condition of the Bank.