Question

9. How much interest is earned in 6 years on $8800 deposited in an account paying 7% interest, compounded semiannually? (Round your answer to two decimal places.)

10.$15,000 is deposited for 8 years in an account earning 6% interest. (Round your answers to two decimal places.)

(a) Calculate the future value of the investment if interest is compounded semiannually.
$

(b) Calculate the future value if interest is compounded quarterly.
$

(c) How much greater is the future value of the investment when the interest is compounded quarterly?
$

11.An amount of $1100 is deposited for 7 years in an account that earns 6% interest. (Round your answers to two decimal places.)

(a) Calculate the simple interest earned.
$

(b) Calculate the interest earned if interest is compounded daily.
$

(c) How much more interest is earned on the account when the interest is compounded daily?
$

12.You borrow $8000 to help pay your college expenses. You agree to repay the loan at the end of 7 years at 10% interest, compounded monthly. (Round your answers to two decimal places.)

(a) What is the maturity value of the loan?
$

(b) How much interest are you paying on the loan?
$

13.A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born in order to have $36,000 when the child reaches the age of 18? Assume the money earns 5% interest, compounded monthly. (Round your answer to two decimal places.)
$

14.Suppose your salary in 2020 is $70,000. Assuming an annual inflation rate of 8%, what salary do you need to earn in 2027 in order to have the same purchasing power? (Round your answer to two decimal places.)

Answer 1

In most of the questions mentioned above, we have been provided with nominal rate of interests i.e. i (p) , where i represents the rate of interest and p represents the number of times the amount being compounded in a year.

Question 9 :-  Present value , PV = $8800 , i (2) = 7% and term , n = 6 years

Accumulated value , AV = PV * ( 1 + i (p) /p )p * n  

= 8800 * ( 1 + 0.07/2 )2*6

   = $13297.40418   $13297.40.

Thus, the total interest earned = AV - PV = 13297.40 - 8800 = $4497.40.

Question 10 :-   Present value , PV = $15000  and term , n = 8 years

a) In this case, i (2) = 6% i.e. interest is accumulated semiannually , p= 2

Thus,

Accumulated value , AV = PV * ( 1 + i (p) /p )p * n  

= 15000 * ( 1 + 0.06/2 )2*8

= $24070.59659 $24070.60

b) In this case, i (4) = 6% i.e. interest is accumulated quaterly, p = 4

Thus,

Accumulated value , AV = PV * ( 1 + i (p) /p )p * n  

= 15000 * ( 1 + 0.06/4 )4*8

= $24154.8648   $24154.87

c) Surplus amount = AV when interest is accumulated quaterly - AV when interest is accumulated semiannually

= $24154.87 -  $24070.60

= $84.27

Question 11 :-   Present value , PV = $11000  and term , n = 7 years

a) In this case, i = 6% as simple interest.

Accumulated value , AV = PV * ( 1 + i * n )

= 11000 * ( 1 + 0.06*7 )

= $15620

Thus, the total interest earned = AV - PV = 15620 - 11000 = $ 4620

b) In this case, i (365) = 6% i.e. interest is accumulated daily, p =365

Thus,

Accumulated value , AV = PV * ( 1 + i (p) /p )p * n  

= 11000 * ( 1 + 0.06/365 )365*7

= $16740.99926 $16741

Thus, the total interest earned = AV - PV = 16741 - 11000 = $ 5741

c) Surplus amount = Total interest earned when interest is accumulated daily - Total interest earned when interest is calculated using simple interest

= 5741 - 4620

= $ 1121

Question 12 :-   Present value of the loan , PV = $8000, i (12) = 10% and term of the loan , n = 7 years

a) Matuarity value of loan = Accumulated values of loan

= PV * ( 1 + i (p) /p )p * n  

   = 8000 * ( 1 + 0.1/12 )12*7

= $16063.36122 $16063.36

Thus, the matuarity value of loan is $16063.36.

b) Total interest payable on loan = AV of loan - PV of loan

   = $16063.36 - $8000

= $8063.36

Question 13 :-   Accumulated value , AV = $36000, i (12) = 5%  and term , n = 18 years

To find :- Present value, PV = ?

Solution :- Since, AV = PV * ( 1 + i (p) /p )p * n  

PV = AV * ( 1 + i (p) /p ) - (p * n)  

= 36000 * ( 1 + 0.05/12 ) - 12 * 18

= $14663.90081 $14663.9

Thus, the principal amount deposited by the parents on the birth of the child is $14663.9

Question 14 :- Here, the current salary is of $70000 and the annual inflation (interest) rate is given as 8%. In order to have the same purchasing power in 2027 as of now, the salary must also accumulate (or increase ) at the same rate of the inflation.Also the rate of interest provided is accumulated annually i.e. we are given the effective rate of interest and thus, the value of p in this case is 1 i.e. i(1) = i

Therefore,

Present value , PV = $70000, i = 8% and term , n = 7 years

Salary required to be earned in 2027 = Accumulated value of the salary in 2020

= 70000 * (1 + 0.08 )7

= $11996.76988 $11996.77

Thus, the salary required to be earned in 2027 in order to have the same purchasing power in 2027 as of now is $11996.77.