If you need $20,000 in your bank account in 6 years, how much must be deposited now? The interest rate is 10%, compounded contin
1 answer:
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Answer:
1. Interest compounded annually = $18,049.74
2. Interest compounded quarterly = $18,493.77
3. Interest compounded Monthly = $18,598.16
4. Interest compounded continuously = $18,651.19
Explanation:
First let me state the formula for compound interest:
The future value of a certain amount which is compounded is the total amount (Principal + interest) on the amount of money, after compound interests have been applied, and this is shown below:
FV = PV
where:
FV = Future value
PV = Present value = $7,000
r = interest rate in decimal = 0.07
n = number of compounding periods per year
t = compounding period in years = 14
For interests compounded continuously, the Future value is given as:
FV = PV ×
where
is a mathematical constant which is = 2.7183
Now to calculate each on the compounding periods one after the other:
1. Interest compounded annually:
here n (number of compounding periods annually) = 1
Therefore,
FV = 7,000 ×
FV = 7,000 × = $18,049.74
2. Interest compounded quarterly:
here, n = 3 ( there are 4 quarters in a year)
FV = 7,000 ×
FV = 7,000 × = $18,493.77
3. Interest compounded Monthly:
here n = 12 ( 12 months in a year)
FV = 7,000 ×
FV = 7,000 × = $18,598.16
4. Interests compounded continuously:
FV = PV ×
FV = 7,000 × 2.66446 = $18,651.19