Question

5. Zane just graduate from college and is thrilled to explore his new life and all the excitement that comes with it. Just now, Zane received communication from a company to whom he owes $100,000 in student loans. The information in the communication states that Zane agreed on an annual interest rate of 7.99 percent that is compounded annually. Also, Zane is allowed to make one fixed payment at the end of each year for the next 10 years. Zane is shocked by this information because it has been 4 years since he signed that agreement but he is not disheartened because he received another email from a company he interviewed with that he has been hired at an above average starting salary. Zane is a planner and he pulls up his old financial calculator to figure out how he is going to be debt free very soon. Although the loan asks for payment at the end of each year, Zane believes that he should not wait all year long and instead should save every month. His expected salary after taxes is $5,000 per month. He has a savings account at a credit union that is expected to pay 3 percent interest on savings that is compounded monthly. Bases in this and any subsequent information, answer the following questions: a. What is the annual payment that Zane must make in order to fulfil the loan terms? b. In order to save this annual payment, Zane has decided to deposit an equal amount of money from his paycheck to his savings account. What should be the monthly amount for Zane to have accumulated the annual payment? c. Suppose that Zane wants to pay off his debt in 5 years instead of 10. Answer options a. and b. based on a 5 year timeline and assuming all the other information from question 5.

Answer 1

(a)      
Time for repayment (n) =   10   years
Interest rate (i)=   7.99%   or 0.0799
      
Amount of loan (P) =   $100,000.00  

Equal annual payments for loan formula = P* i *((1+i)^n)/((1+i)^n-1)      
100000*0.0799*((1+0.0799)^10)/(((1+0.0799)^10)-1)      
14,896.23      

So, equal annual payments will be    $14,896.23  

(B)

Amount to be accumulated(Future value)=   $14,896.23   

To save annual Amount, Time in months (n) =   12  
Interest rate (i)= 3%/12=   0.0025  

Future value of annuity formula = P *{ (1+r)^n - 1 } / r      
      
14896.23 = P*(((1+0.0025)^12)-1)/0.0025      
14896.23 = P*   12.16638277  
p=   1224.376045  

So, equal Monthly Savings Required to accumulate annual amount is   $1,224.38  

(C) timeline = 5 years

Time for repayment (n) =   5   years
Interest rate (i)=   7.99%   or 0.0799
      
Amount of loan (P) =   $100,000.00  

Equal annual payments for loan formula = P* i *((1+i)^n)/((1+i)^n-1)      
100000*0.0799*((1+0.0799)^5)/(((1+0.0799)^5)-1)      
25,039.04      

So, equal annual payments will be    $25,039.04  

(D)

(b) Amount Required to accumulate (Future value)=   $25,039.04
To save annual Amount, Time in months (n) =   12
Interest rate (i)= 3%/12=   0.0025

Future value of annuity formula = P *{ (1+r)^n - 1 } / r  
  
25039.04 = P*(((1+0.0025)^12)-1)/0.0025  
25039.04 = P*   12.16638277
p=   2058.051698

So, equal Monthly Savings Required to accumulate annual amount is   $2,058.05
  

Please thumbs up or post comments if any query.