Answer: a) $481.62 b) $16,569.76
Step-by-step explanation:
The formula for compound interest is: [tex]A = P(1 + r)^t[/tex] where
- A is the accrued amount (balance)
- P is the principle (initial deposit)
- r is the rate (convert percentage into a decimal)
- t is the time (number of years)
Given: P = 3000, r = 1.15% (0.015), t = 10
[tex]A = 3000(1 + 0.015)^{10}\\\\\\A = 3000(1.015)^{10}\\\\\\A = 3,481.62[/tex]
Interest Earned = accrued amount - principle
= 3,481.62 - 3,000
= 481.62
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I couldn't remember the formula so I created a table:
[tex]\begin{array}{c||l|c||r}\underline{Jan\ 1}&\underline{Interest\ Earned}&\underline{Deposit}&\underline{Balance}\\2019&0&3000&3,000.00\\2120&3000(1.015)&1200&4,245.00\\2121&4245(1.015)&1200&5,508.68\\2122&5508.68(1.015)&1200&6,791.31\\2123&6791.31(1.015)&1200&8,093.17\\2124&8093.17(1.015)&1200&9,414.57\\2125&9414.57(1.015)&1200&10,755.79\\2126&10755.79(1.015)&1200&12,117.13\\2127&12117.13(1.015)&1200&13,498.88\\2128&13498.88(1.015)&1200&14,901.37\\2129&14901.37(1.015)&1200&16,324.89\\\end{array}[/tex]
2130 || 16324.89(1.015) | 0 || 16,569.76
