Question

Kiara opened an RRSP deposit account on December 1, 2008 with a deposit of $1,700. She added $1,700 on January 1, 2010, and $1,700 on May 1, 2012. How much is in her account on December 1, 2016 if the deposit earns 5.6% p.a. compounded monthly? Select one: a. $7,242.55 b. $7,289.55 c. $7,341.64 d. $7,356.28

Answer 1

Answer:

The total balance on December 1, 2016 is B = $7356.28

Step-by-step explanation:

I am going to call B1 the balance for the first deposit, B2 the balance for the second deposit and B3 for the third deposit.

This is a compound interest problem.

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

A: Amount of money(Balance)

P: Principal(Initial deposit)

r: interest rate(as a decimal value)

n: number of times that interest is compounded per unit t

t: time the money is invested or borrowed for.

First step: Balance B1 on December 1, 2016

A = amount of money =  B1

P = 1,700

r = 0.056

n = 12(compounded mothly, and t is in years)

t = 8 years

$B1 = 1700(1 + \frac{0.056}{12})^{96}$

$B1 = 2658.17$

Second step: Balance B2 on December 1, 2016

A = B3

P = 1,700

r = 0.056

n = 12(compounded mothly, and t is in years)

t: From January 1, 2010 to December 1, 2016 there are 6 years and 11 months. 11 months is 0.92 of a year. So

t = 6.92

$B2 = 1700(1 + \frac{0.056}{12})^{83.04}$

$B2 = 2502.39$

Third step: Balance B3 on December 1, 2016

A = B3

P = 1700

r = 0.056

n = 12

t: 4 years and 7 months. 7 months is 7/12 = 0.58. So t = 4.58 years.

$B3 = 1700(1 + \frac{0.056}{12})^{54.96}$

$B3 = 2195.72$

Final step: Total balance on December 1, 2016

B = 2195.72 + 2502.39 + 2658.17

B = $7356.28

So the total balance on December 1, 2016 is B = $7356.28