Question

Compute the future value of a $160 cash flow for the following combinations of rates and times. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

a. r = 8%; t = 10 years

b. r = 8%; t = 20 years

c. r = 4%; t = 10 years

d. r = 4%; t = 20 years

Answer 1

For calculating the future value, we will use the following formula:

FV= P * (1+ r%)ⁿ

where, FV= Future value, P= Principal amount, R = Rate of interest and n= time period

(a) r = 8%, t= 10 years, P= $160

Now, putting these values in the above formula, we get,

FV = $160 * (1 + 8%)¹⁰

FV = $160 * (1 + 0.08)¹⁰

FV = $160 * (1.08)¹⁰

FV = $160 * 2.15892499727

FV = $345.43, which is the required future value.

(b) r = 8%, t= 20 years, P= $160

Now, putting these values in the above formula, we get,

FV = $160 * (1 + 8%)²⁰

FV = $160 * (1 + 0.08)²⁰

FV = $160 * (1.08)²⁰

FV = $160 * 4.66095714385

FV = $745.75, which is the required future value.

(c) r = 4%, t= 10 years, P= $160

Now, putting these values in the above formula, we get,

FV = $160 * (1 + 4%)¹⁰

FV = $160 * (1 + 0.04)¹⁰

FV = $160 * (1.04)¹⁰

FV = $160 * 1.48024428492

FV = $236.84, which is the required future value.

(d) r = 4%, t= 20 years, P= $160

Now, putting these values in the above formula, we get,

FV = $160 * (1 + 4%)²⁰

FV = $160 * (1 + 0.04)²⁰

FV = $160 * (1.04)²⁰

FV = $160 * 2.19112314303

FV = $350.58, which is the required future value.