Answer to Question #169080 in Financial Math for saleemaslam

Question

Due: March 5,2021 @ 12:00pmBusiness Mathematics       Kwantlen Polytechnic University            Quiz #3                              Name: _______________  Student ID: ___________   Mark: __/10                 

 

Note: 1. Answer all questions in space provided.

 2. Show your work to receive full marks.

 3. Be sure to upload your completed work as Word Document;

 4. No other format will be accepted (incl. .pages).

1. Sally invested $1,750 into an RRSP that earned interest at 5% compounded semiannually for eight years.

   a. Determine the balance of the account at the end of the period? _____________      

   b. How much interest is earned? ______________

c. What is the effective rate? _____________

 

2. Suppose an investment of $800 earned interest of $320 at 6% compounded monthly. For how many years was the money invested?   ___________________

 

 

 

3. Mark made ordinary annuity payments of $15 per month for 16 years, earning 4.5% compounded monthly.

    a. How much will be the accumulated value (future value) after 16 years?  __________

    b. How much of the accumulated value is interest? _______________

 

 

 

 

4. A loan was repaid over seven years by end-of-month payments of $450. If interest was 12% compounded monthly, how much interest was paid?  _______________

 

 

 

 

5. What is the size of the monthly deposits that will accumulate to $67,200 after eight years at 6.5% compounded semiannually? _________________

 

 

 

 

 

The End

Answer 1

1.

a. $FV=PV(1+r)^n$

PV=1750

$r=\frac{0.05}{2}=0.025$

$n=2\times8=16$

$FV=PV(1+r)^n=1750(1+0.025)^{16}=2597.88$

b. interest=2597.88-1750=848.88

c.$EAR=(1+\frac{r}{n})^n-1=(1+\frac{0.05}{2})^2-1=0.0506$ or 5.06%

2.$FV=PV(1+r)^n$

$n=\frac{log(\frac{FV}{PV})}{m(log(1+\frac{r}{m)}}=\frac{log(\frac{800}{320})}{12(log(1+\frac{0.06}{12})}=\frac{0.3979}{0.02599}=13.3$

3.

a. $FV=A\frac{(1+r)^n-1}{r}$

A=15

$r=\frac{0.045}{12}=0.00375$

$n=16\times12=192$

$FV=15\frac{(1+0.00375)^{192}-1}{0.00375}=4206.67$

b. $interest=4206.67-15\times192=1326.67$

4.

$x=PV(r+\frac{r}{(1+r)^n-1})$

x=450

$n=7\times12=84$

$r=\frac{0.12}{12}=0.01$

$450=PV(0.01+\frac{0.01}{(1+0.01)^{84}-1})$

450=0.01765PV

PV=25495.75

$interest=450\times84-25 495.75=12304.25$

5.$FV=A\frac{(1+r)^n-1}{r}$

FV=67 200

n=8

r=0.065

$67200=A\frac{(1+0.0065)^{8}-1}{0.0065}$

67200=8.18A

A=8215.16