Solution a:
Future value after 2 years = $5,000 (1+0.06)^2 = $5,618
Solution b:
Future value after 7 years = $5,618 (1+0.08)^5 = $5,618 * 1.469238 = $8,254.69
Solution c:
Future value after 12 years = $8,254.69 (1+0.07)^8 = $8,254.69 * 1.718186 = $14,183.09
SOLUTION :
a.
Amount deposited at year 0 :
Interest rate for first two years is 6% (0.06 in decimals)
So, Amount at year 2 end :
= 5000 * (1 + 0.06)^2
= 5618 ($) (ANSWER)
b.
Amount in the account at year 2 end = 5618 ($)
Interest rate for next 5 years is 8% (0.08 in decimals)
So, Amount at the end of year 7 :
= 5618 * (1 + 0.08)^5
= 8254.69 ($) (ANSWER)
c.
Amount in the account at year 7 end = 8254.69 ($)
Interest rate for next 8 years (from end of 7 years to end of 15 years)
is 7% (0.07 in decimals)
So, Amount at the end of 15 years
= 8254.69 * ( 1 + 0.07)^8
= 14183.09 ($) (ANSWER).
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