Compound interest is interest that is calculated on both the money deposited and the interest earned from that deposit.
The formula for compound interest is A=P(1+rn)nt, where A represents the final balance after the interest has been calculated for the time, t, in years, on a principal amount, P, at an annual interest rate, r. The number of times in the year that the interest is compounded is n.
Jasmine deposits $520 into a savings account that has a 3.5% interest rate compounded monthly. What will be the balance of Jasmine’s savings account after two years?
To find the balance after two years, A, we need to use the formula, A=P(1+rn)nt. The principal, P, in this situation is the amount Jasmine used to start her account, $520. The rate, r, as stated in the problem, is 3.5% (or 0.035 as a decimal) and compounded monthly, so n=12. Since we are looking for the balance of the account after two years, 2, is the time, t.
A=520(1+0.03512)12(2) A=557.65
The balance of Jasmine’s account after 2 years is $557.65.
Example 2:
Lex has $1,780.80 in his savings account that he opened 6 years ago. His account has an annual interest rate of 6.8% compounded annually. How much money did Lex use to open his savings account?
To find the principal, P we can use the same formula, A=P(1+rn)nt. We have the balance of the account, A, after 6 years, which is $1,780.80. The interest rate, r, is 6.8% (or 0.068 as a decimal) and is compounded annually, so n=1. The time, t, is 6, since we know he opened his account 6 years ago. Plug in the known values into the formula and solve for the missing variable, P.
1,780.80=P(1+0.0681)1(6) 1,780.80=1.484P 1,200=P
The principal amount Lex used to open his account 6 years ago is $1,200.
Compound Interest Sample Questions
Question #1:
A teacher wants to invest $30,000 into an account that compounds annually. The interest rate at this bank is 1.8%. How much money will be in the account after 6 years?
$43,389.35
$35,389.35
$33,389.35
$37,389.35
Answer:
Use the compound interest formula to solve this problem.
A=P(1+rn)nt
From here, simply plug in each value and simplify in order to isolate the variable A.
An investment earns 3% each year and is compounded monthly. Calculate the total value after 6 years from an initial investment of $5,000.
$5,114.74
$4,984.74
$5,984.74
$2,984.74
Answer:
Once again, use the compound interest formula to solve this problem.
A=P(1+rn)nt
From here, simply plug in each value and simplify in order to isolate the variable A.
A=5,000(1+0.031212×6 A=5,000(1.36)72 A=$5,984.74
Question #3:
Kristen wants to have $2,000,000 for retirement in 45 years. She invests in a mutual fund and pays 8.5% each year, compounded quarterly. How much should she deposit into the mutual fund initially?
$47,421.08
$35,421.08
$43,421.08
$45,421.08
Answer:
Once again, use the compound interest formula to solve this problem.
A=P(1+rnnt
From here, simply plug in each value and simplify in order to isolate the variable P.