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Question 1 (6 marks) Mr. Clark made deposits of $950 at the end of every 6...

Question 1

Mr. Clark made deposits of $950 at the end of every 6 months for 15 years. If interest is 3% compounded monthly and if he leaves the accumulated balance for another 10 years, what will be the balance in his account then? (i.e. 10 years after the last deposit) _______________

How much of the accumulated amount is interest? _____________

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Solutions

Expert Solution

Eeffective 6 Months Rate = ( 1 + r)^n - 1

= ( 1 + 0.0025)^6 - 1

= ( 1.0025^6 ) - 1

= 1.015094 - 1

= 0.015094 i.e 1.5094%

FV aof Annuity after 15 Yeras:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	950
Int Rate	1.509%
Periods	30

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r

= $ 950 * [ [ ( 1 + 0.01509 ) ^ 30 ] - 1 ] / 0.01509

= $ 950 * [ [ ( 1.015094 ) ^ 30 ] - 1 ] / 0.015094

= $ 950 * [ [1.5674] - 1 ] / 0.015094

= $ 950 * [0.5674] /0.015094

= $ 35713.35

FV after 10 Years :

FV = PV (1+r)^n
Where n is Int rate per period
n - No. of periods
= $ 35713.35 * ( 1 + 0.015094 )^ 20

= $ 35713.35 * ( 1.015094 )^ 20

= $ 35713.35 * 1.3494

= $ 48189.94

Int = FV after 25 Years - [ Deposits Made ]

= $ 48189.94 - [ $ 950 * 30 ]

= $ 48189.94 - [ $ 28500 ]

= $ 19689.94

Pls do rate, if the answer is correct and comment, if any further assistance is required.

jeff jeffy answered 1 year ago

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