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goldenfox [79]
3 years ago
9

Find a recurrence relation for the amount of money in a savings account after n years if the interest rate is 6 percent and $50

is added at the start of each year.
Mathematics
1 answer:
Korvikt [17]3 years ago
3 0

Answer:

a_n = a_{n-1} (1.06) + 50

Step-by-step explanation:

Suppose, a_0 is initial amount in the saving account,

Here, the annual interest rate is 6% and additional amount in each year is $ 50,

So, the amount after one year,

a_1 = a_0 + 6\%\text{ of }a_0 + 50 = a_0 + 0.06a_0 + 50 = a_0(1.06) + 50

Amount after 2 years,

a_2 = a_1 + 6\%\text{ of }a_1 + 50 = a_1(1.06) + 50

Amount after 3 years,

a_3 = a_2 + 6\%\text{ of }a_2 + 50 = a_2(1.06) + 50

................................., so on....

Hence, by following the pattern,

The amount after n years,

a_n = a_{n-1} (1.06) + 50

Which is the required recurrence relation for the amount of money in a savings account

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