Question

Question 4 of 13 Corey's grandmother is depositing $1,200 at the end of each quarter into a RESP to save for Corey's University education. The RESP earns interest at 5.50% compounded quarterly. Corey will start university in six years at which time his grandmother will stop contributing. a. How much will grandmother have accumulated in the RESP in six years? $0.00 Round to the nearest cent b. How much can Corey withdraw from his RESP at the end of each quarter for four years? $0.00 Round to the nearest cent

Answer 1

(a) Here, the deposits will be same every quarter, so it is an annuity. We need to calculate the future value of annuity. We will use the following future value of annuity formula:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity, P is the periodical amount = $1200, r is the rate of interest = 5.5% and n is the time period = 6 * 4 = 24 quarters

Now, putting these values in the above formula, we get,

FVA = $1200 * ((1 + 5.5%)24 - 1 / 5.5%)

FVA = $1200 * ((1 + 0.055)24 - 1 / 0.055)

FVA = $1200 * ((1.055)24 - 1 / 0.055)

FVA = $1200 * ((3.61458990391 - 1 / 0.055)

FVA = $1200 * (2.61458990391 / 0.055)

FVA = $1200 * 47.5379982528

FVA = $57045.60

So, after 6 years, RESP will have accumulated amount of $57045.60.

(b) Here, the withdrawals will be same every quarter, so it is an annuity. Here, we will use the following formula of  present value of annuity:

PVA = P * (1 - (1 + r)-n / r)

where, PVA = Present value of annuity = $57045.60, P is the periodical amount, r is the rate of interest = 5.5% and n is the time period = 4 * 4 = 16 quarters

Now, putting these values in the above formula, we get,

$57045.6 = P * (1 - (1 + 5.5%)-16 / 5.5%)

$57045.6 = P * (1 - ( 1+ 0.055)-16 / 0.055)

$57045.6 = P * (1 - ( 1.055)-16 / 0.055)

$57045.6 = P * (1 - 0.42458108825) / 0.055)

$57045.6 = P * ($0.57541891175 / 0.055)

$57045.6 = P * 10.462162031818

P = $57045.6 / 10.462162031818

P = $5452.56

So, Corey can withdraw $5452.56