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# Compound Interest

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Compound Interest.
For the next two problems apply formula: A = P(1 + i)n and use scientific calculator.
I - interest rate per period in decimal form, annual rate divided by number of periods per year
P - deposit
n -total number of deposits over all given years

Problem 1. Retirement Funds
Five and a half years ago, Chris invested \$10,000 in a retirement fund that grew at the rate of 10.82%/year compounded quarterly. What is his account worth today?

Problem 2. Investment Options.
Investment A offers a 10% return compounded semiannually, and investment B offer a 9.75% return compounded continuously. What investment has a higher rate of return over a 4 year period?

Continuous Interest.
For the next two problems apply formula: A =P e^it and use scientific calculator.
I - annual interest in decimal form
P - deposit
t - number of years

Problem 3.
\$1,000 was debited on account that has continuous interest with annual interest rate 2%. How much will be on this account after 5 years?

Problem 4.
Let's say you put in a bank \$5,000. How much will be on your account in 10 years if bank calculates continuous interest with annual interest rate 3%?

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Mortgage monthly payment.
For the next two problems apply formula: R = (i*P)/〖1- (1+i)〗^(-n) and use scientific calculator.
I - interest rate per month in decimal form, annual rate in decimal form divided by 12
P - principal, amount you borrow from bank
n -total number of payments over all given years
If you have problem with your calculator to find (1+i)^(-n)
find (1+i)^n first and then divide 1 by this value.
For example, find (1+0.02)^(-120) .
Using y^x function on calculator find (1+0.02)^120 = (1.02)^120 = 10.765
Then (1.02)^(-120) = 1 /10.765 = 0.09289

Problem 5.
Calculate monthly payment on a mortgage \$200,000.00 over 10 years. Annual percentage rate is 4.8%

Problem 6.
Price for the house is \$400,000. You paid \$40,000 as down payment and the rest took as mortgage. Calculate monthly payment on this mortgage over 30 years. Annual percentage rate is 6%.

#### Solution Preview

See the attached file.

Compound Interest.
For the next two problems apply formula: A = P(1 + i)n and use scientific calculator.
I - interest rate per period in decimal form, annual rate divided by number of periods per year
P - deposit
n -total number of deposits over all given years
Problem 1.

For this problem we first need to define the variables that will be used:

I = 10.82% = 0.1082
P = \$10,000
n = 5.5(4) = 22 (this is because there are 4 quarters in a year)

Next we just substitute the values into the equation above:

A = P(1 + i)n
A = 10,000(1 + 0.1082)22
A = 10,000(1.1082)22
A = 10,000(9.58516)
A = 95,850.16

So 5.5 years from the initial deposit his investment would be worth \$95,850.16

Problem 2.

It appears that this problem wants us to compare the two different loans. This is a little different as each loan will use a different formula. The first one compounds semiannually so we will use: ...

#### Solution Summary

This solution addresses compounded interest in different finance problems.

\$2.19