Answer:
Additional Earnings = $3386.940745 rounded off to $3386.94
Explanation:
To calculate the amount of additional income, we must first calculate the interest earned at 5% and 6% semi annual compounding for 7 years and then deduct the interest earned at 6% from the interest earned at 5%. The formula to calculate the interest earned under semi annual compounding is,
Interest earned = Principal * (1 + i/n)^(t*n) - Principal
Where,
As the compounding is done semi annually, we can say that the interest is compounded 2 times in a year. Thus, n = 2
At 5 % semi annual compounding
Interest earned = 34000 * (1 + 0.05/2)^(7*2) - 34000
Interest earned = $14041.1099 rounded off to $14041.11
At 6 % semi annual compounding
Interest earned = 34000 * (1 + 0.06/2)^(7*2) - 34000
Interest earned = $17428.05065 rounded off to $17428.05
Additional earnings = 17428.05065 - 14041.1099
Additional Earnings = $3386.940745 rounded off to $3386.94
The additional income that Jonathan could earn with 6% over 5% interest is $9,908.71.
Explanation:
N (# of periods) = 14 (7 x 2)
I/Y (Interest per year) = 5%
PV (Present Value) = $34,000
PMT (Periodic Payment) = $0
Settings
P/Y (# of periods per year) = 1
C/Y (# of times interest compound per year) = 2
PMT made at the of each period = $0
Results:
FV = $67,880.83
Total Interest $33,880.83
N (# of periods) = 14 (7 x 2)
I/Y (Interest per year) = 5%
PV (Present Value) = $34,000
PMT (Periodic Payment) = $0
Settings
P/Y (# of periods per year) = 1
C/Y (# of times interest compound per year) = 2
PMT made at the of each period = $0
Results:
FV = $77,789.54
Total Interest $43,789.54
Thus, the additional income with 6% over 5% interest is $9,908.71 ($43,789.54 - $33,880.83).
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