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# Mathematics - Other

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Calculate the compound interest for the following:

\$10,000 invested for 10 years at 10% compounded annually

\$4,000 invested for 7 years at 8% compounded annually

Calculate the present value for the following:

\$400 to be received 10 years from now discounted back to the present at 10%

\$600 to be received 5 years from now discounted back to the present at 5%

#### Solution Preview

(1) P = 10000, r = 10% = 0.10, t = 10

A = P(1 + r)^t

A = 10000(1 + 0.10)^10 = \$25937.42

CI = A - ...

#### Solution Summary

A Complete, Neat and Step-by-step solution is provided.

\$2.19

## Discrete Math: Integers

A US Social Security number is a nine-digit number. The first digit (or digits) may be zero.
a) How many US Social Security numbers are available?
b) How many US Social Security numbers are odd?
c) How many US social security numbers read the same backward and forward (eg 350767053)?

a) How many 4-digit numbers do not contain number 5 among its digits?
b) How many 4-digit numbers contain at least one number 5 among its digits?
c) How many 4-digit numbers contain exactly one number 5 among its digits?

Prove that if a is an odd integer, then a^2 + 7 is divisible by 4.

Read very carefully each of these sentences. Then, complete them:
a) The only integer which is divisible by every other integer is...
b) The integers that divide all prime numbers are ... and ...
c) If p is a prime number, it has ... positive divisors, and ... integer divisors.
d) (See the attachment for the equation)
e) Which one is larger, 2^1000 or 500! ? The answer is ...
f) The set {{2,6},{3,6}} has exactly ... elements. Does it coincide with {2,3,6}?

Prove that 99^4 divides 100!-99!

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