Question

9. For the past four years, Joely authorized the payroll department at her work to deduct $30 per week to be placed into an RRSP account. If interest is 5.17% compounded monthly, how much has Joely accumulated in her RRSP?

10. Clark's younger brother saved $18 per month from his paper route for the past two years. If interest is 4% compounded quarterly, how much will he have accumulated in his savings account?

Answer 1

To calculate the amount accumulated in Joely's RRSP account, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amount accumulated

P = the initial contribution per week ($30)

r = interest rate per year (5.17% or 0.0517)

n = number of times the interest is compounded per year (12 for monthly compounding)

t = number of years (4)

Substituting the values into the formula, we have:

A = 30(1 + 0.0517/12)^(12*4)

Simplifying the equation within the parentheses:

A = 30(1.0043083)^(48)

Calculating the value within the parentheses:

A = 30(1.231193238)

Multiplying the result by the initial contribution per week:

A = $36.93579714

Therefore, Joely has accumulated approximately $36.94 in her RRSP account over the past four years.

To calculate the amount accumulated in Clark's younger brother's savings account, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amount accumulated

P = the initial contribution per month ($18)

r = interest rate per year (4% or 0.04)

n = number of times the interest is compounded per year (4 for quarterly compounding)

t = number of years (2)

Substituting the values into the formula, we have:

A = 18(1 + 0.04/4)^(4*2)

Simplifying the equation within the parentheses:

A = 18(1.01)^(8)

Calculating the value within the parentheses:

A = 18(1.08367498)

Multiplying the result by the initial contribution per month:

A = $19.50514964

Therefore, Clark's younger brother will have accumulated approximately $19.51 in his savings account over the past two years.