Question

1. If you receive $176 each month for 12 months and the discount rate is 0.04, what is the future value?

(show the process and can use financial calculator)

2. If you receive $249 each quarter for 4 quarters and the discount rate is 0.08, what is the present value?

(show the process and can use financial calculator)

3. If you receive $98 each month for 12 months and the discount rate is 0.07, what is the present value?

(show the process and can use financial calculator)

4. If you receive $116 each month for 28 years and the discount rate is 0.08, what is the present value?

(show the process and can use financial calculator)

5. If you receive $136 each 6 months for 3 years and the discount rate is 0.03, what is the future value?

(show the process and can use financial calculator)

Answer 1

1.

Amount received each month = P = $176

Monthly Interest Rate = r = 0.04/12

Number of months = n = 12

Future Value = FV = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P

= P[(1+r)ⁿ -1]/r

= 176[(1+0.04/12)¹² -1]/(0.04/12)

= $2151.15

2.

Amount received each quarter = P = $249

Quarterly Interest Rate = r = 0.08/4

Number of quarters = n = 4

Present Value = PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ

= P[1- (1+r)^-n]/r

= 249[1- (1+0.08/4)^-4]/(0.08/4)

= $948.12

3.

Amount received each month = P = $98

monthly Interest Rate = r = 0.07/12

Number of months = n = 12

Present Value = PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ

= P[1- (1+r)^-n]/r

= 98[1- (1+0.07/12)^-12]/(0.07/12)

= $1132.60

4.

Amount received each month = P = $116

monthly Interest Rate = r = 0.08/12

Number of months = n = 28

Present Value = PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ

= P[1- (1+r)^-n]/r

= 116[1- (1+0.08/12)^-28]/(0.08/12)

= $2953.92

5.

Amount received every 6 months = P = $136

Semiannual Interest Rate = r = 0.03/2

Number of semiannual periods = n = 3*2 = 6

Future Value = FV = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P

= P[(1+r)ⁿ -1]/r

= 136[(1+0.03/2)⁶ -1]/(0.03/2)

= $847.22