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$5,000 is deposited today into a bank account. The account earns 7.1% per annum compounded half...

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Finance

$5,000 is deposited today into a bank account. The account earns7.1% per annum compounded half yearly for the first 6 years, then4.2% per annum compounded quarterly thereafter. Assuming no furtherdeposits or withdrawals are made, (a) Calculate the account balancesix months from today. (b) Calculate the account balance 6 yearsfrom today. (c) Calculate the account balance 6.5 years from today.(d) Calculate the account balance 10 years from today.

Answer & Explanation Solved by verified expert
3.6 Ratings (338 Votes)

(a) Account balance six months from today = Amount invested * Future value of 1
= $ 5,000.00 * 1.0355
= $ 5,177.50
Working:
Future value of 1 = (1+0.0355)^1 Where,
= 1.0355 i 7.1%/2 = 0.0355
n = 1
(b) Account balance 6 years from today = Amount invested * Future value of 1
= $ 5,000.00 * 1.519852
= $ 7,599.26
Working:
Future value of 1 = (1+0.0355)^12 Where,
= 1.5198518 i 7.1%/2 = 0.0355
n 6*2 = 12
(c) Account balance 6.5 years from today = Amount invested * Future value of 1
= $ 7,599.26 * 1.02111
= $ 7,759.68
Working:
Future value of 1 = (1+0.0105)^2 Where,
= 1.0211103 i 4.2%/4 = 0.0105
n = 2
(d) Account balance 6.5 years from today = Amount invested * Future value of 1
= $ 7,599.26 * 1.181901
= $ 8,981.57
Working:
Future value of 1 = (1+0.0105)^16 Where,
= 1.181901 i 4.2%/4 = 0.0105
n 4*4 = 16
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