Compound Interest Calculation: Chen's RRSP Deposit Account
How much is in Chen's RRSP deposit account on September 1, 2016?
Chen opened an RRSP deposit account on December 1, 2008, with a deposit of $2300. He added $2300 on August 1, 2010, and $2300 on December 1, 2012. Given that the deposit earns 6.8% p.a compounded monthly, what is the total amount in his account on September 1, 2016?
Answer:
The amount in Chen's RRSP deposit account on September 1, 2016, is approximately $3816.02.
To calculate the amount in Chen's RRSP deposit account on September 1, 2016, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Given:
Principal (P) = $2300
Annual interest rate (r) = 6.8% = 0.068 (in decimal form)
Interest is compounded monthly, so n = 12 (12 times per year)
t = 2016 - 2008 = 8 years (from December 1, 2008, to September 1, 2016)
Using the formula:
A = $2300(1 + 0.068/12)^(12*8)
Calculating the expression inside the parentheses:
(1 + 0.068/12) = 1.00566667 (rounded to 8 decimal places)
Plugging in the values:
A = $2300(1.00566667)^(96)
Calculating the final amount:
A ≈ $2300(1.65892460)
Therefore, the total amount in Chen's RRSP deposit account on September 1, 2016, is approximately $3816.02.