Question

7) Alice deposits 50,000.00 in her bank account. Interest is calculated and compounded semi-annually. The interest rate is 8.25% in the first year, 0.50% in the second year, and 2.75% in the third year. At the end of three years Alice will have in her bank account a total balance of s calculated 1178859_answer 8) A deposit of $100.000 is made to an investment account today. At the end of each of the next four years. 55000 must be paid out to a beneficiary, and the account liquidated at the end of year four. If the liquidation value is $100.000 the account has earned an annual internal rate of return of?

Answer 1

7)

Given,

Initial deposit = $ 9000

Compounding periods (n) = 2 per year

First year interest rate = 8.25%

Semi annual rate (r₁) = 8.25% $\div$ 2 = 4.125% or 0.04125

Second year interest rate = 0.50%

Semi annual rate (r₂) = 0.50% $\div$ 2 = 0.25% or 0.0025

Third year interest rate = 2.75%

Semi annual rate (r₃) = 2.75% $\div$ 2 = 1.375% or 0.01375

Solution :-

First year – Initial Interest deposite - $9000/(1+0.0412S)? -;] = $9000 [[1.041255-1] = $9000 (1.08470156 - ] = $ 9000 (0.08420156] = $757.81404 Balance at the end of 1st year (B) = Initial deposit & First year Interest - 89000 + $757.81404 = $9757.81404 second year - B, 11 +82) - ] Interest - $9757.81404 [11+0.0025) - = $9757.8 1404(1.00.29?-1] = $9757.81404 (1.00500625 -1] = $9757.81404 [0.00500625]

- $48.850osos Balance at the end of and year (B2) - B - Second year Interest = $9757.81404 + $48.85 oosos - $9806.66 40965 Third year - B2 [(1+ 8) - ] Interest = $9806.6640965 (1+0. 013709 - 1] 549806.6640965[1.01375) * -] = $9806.6640965 (1.02768906 - 1] - $9806.6640965 [0.02768906] 1.5373 10567 Now, Balance at the end of third year - B + Third year interest - $9806.6640965 + $271.537310567 - $10078.20

Thus, at the end of three years, Alice will have in her bank account a total balance of $ 10078.20