What is the accumulated value if the money is compounded​ quarterly?

Question

Use the compound interest formulas

A=P1+rnnt

and

A=Pert

to solve the problem given. Round answers to the nearest cent.

Find the accumulated value of an investment of

$10,000

for

5

years at an interest rate of

4.5%

if the money is a. compounded​ semiannually;

b.

compounded​ quarterly;

c.

compounded​ monthly; d. compounded continuously.

Answer 1

A = P(1 + r/n)^nt for compounding interest. A is the amount in the account after t years; P is the initial deposit (principal); r is annual interest rate; n is the no. of componding periods/yr and t is the no. of years.

For annual compounding, n = 1, so the formula simplifies to A = P(1 + r)^t.

All the compounding formula does is break the annual interest rate down into a rate per compounding period and change the exponent to the total no. of compounding periods. For example, in this problem for 4.5% annual interest compounded monthly for 5 years, r/n would be 0.045/12 = 0.00375 and the exponent nt would become 12 x 5 = 60 total compounding periods.

Don't forget to use order of operations: add the values within the parentheses first, then apply the exponent and finally, multiply by P. For the monthly compounding, see if you can get the answer of $12,517.96 rounded to the nearest cent. If you get that one correctly, you should be able to do the other compounding periods as well, except for continuous compounding.

For continuous compounding, the formula is A = P x e^rt where e ≅ 2.7183.