Mr. and Mrs. Fox have each contributed $1825.00 per year for the last eight years into RRSP accounts earning 6.93% compounded annually. Suppose they leave their accumulated contributions for another five years in the RRSP at the same rate of interest.
a) How much will Mr. and Mrs. Fox have in total in their RRSP accounts?
b) How much did the Fox's contribute?
c) How much will be interest??
a) the period where they are making deposits is a future value annuity, so use the future value annuity formula to find out how much is in the account after 8 years:
FV = R[(1+I)^n]/i
(Remember that the regular deposit, R, is 2*1875)
The period where their money sits and collects interest is a compound interest situation. Use the formula:
A = P(1+i)^n
(Use the FV value you obtained above, as P)
b) add up how much they both deposited over the 8 years.
c) answer to a) - answer to b)
To answer these questions, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount (initial contribution)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Let's go step by step:
a) To calculate the total amount in their RRSP accounts after 8 years, we can use the formula mentioned above.
- For Mr. Fox:
P = $1825, r = 6.93% (or 0.0693 as a decimal), n = 1 (compounded annually), and t = 8.
Plugging these values into the formula, we get:
A = $1825(1 + 0.0693/1)^(1*8) ≈ $1825(1.0693)^8 ≈ $2,791.33 (rounded to two decimal places).
- For Mrs. Fox:
P = $1825, r = 6.93% (or 0.0693 as a decimal), n = 1 (compounded annually), and t = 8.
Plugging these values into the formula, we get:
A = $1825(1 + 0.0693/1)^(1*8) ≈ $1825(1.0693)^8 ≈ $2,791.33 (rounded to two decimal places).
The total amount in their RRSP accounts after 8 years will be the sum of the amounts for Mr. and Mrs. Fox:
Total = $2,791.33 + $2,791.33 ≈ $5,582.66 (rounded to two decimal places).
b) To find out how much the Foxes contributed in total, we can multiply the annual contribution by the number of years:
Total Contribution = Annual Contribution * Number of Years
Total Contribution = $1825 * 8 = $14,600.
Therefore, the Foxes contributed a total of $14,600.
c) To calculate the amount of interest earned, we need to subtract the total contribution from the total amount in their RRSP accounts:
Interest = Total Amount - Total Contribution
Interest = $5,582.66 - $14,600 ≈ -$9,017.34 (rounded to two decimal places).
The negative value indicates that the Foxes haven't earned any interest yet. This is because they haven't reached the end of the additional five years mentioned in the question. The interest will be calculated for the additional five years separately.
Hope this helps! Let me know if you have any further questions.