Question

unuldu Assignment Save Score: 0 of 4 pts P5-2 (similar to) 2 of 12 (1 complete) HW Score: 8%, 4 of 50 pts Question Help (Related to Checkpoint 5.2) (Future value) Leslie Mosallam, who recently sold her Porsche, placed $10.400 in a savings account paying annual compound interest of 4 percent. a. Calculate the amount of money that will accumulate if Leslie leaves the money in the bank for 37 and 17 year(s) b. Suppose Leslie moves her money into an account that pays 6 percent or one that pays 8 percent Rework part (a) using 6 percent and 8 percent c. What conclusions can you draw about the relationship between interest rates, time, and future sums from the calculations you just did? a. After placing $10.400 in a savings account paying annual compound interest of 4 percent, the amount of money that will accumulate if Leslie leaves the money in the bank for 3 year(s) is (Round to the nearest cent.) Enter your answer in the answer box and then click Check Ans 9 Pemaining Clear All

Answer 1

a)

this question can be solved using future value formula

future value = present value(1 + r)^n

here r = interest rate

n= number of years

accumulation value:

3 years:

future value = present value(1 + r)^n

here r = 4%

n= 3 years

present value = $10,400

so future value = 10,400(1 + 4%)^3

= 10,400(1.04)^3

accumulated value = 10,400 x 1.124864 = $11,248.64

7 years:

future value = present value(1 + r)^n

here r = 4%

n= 7 years

present value = $10,400

so future value = 10,400(1 + 4%)^7

= 10,400(1.04)^7

accumulated value = 10,400 x 1.31593 = $13,685.69

17 years:

future value = present value(1 + r)^n

here r = 4%

n= 17 years

present value = $10,400

so future value = 10,400(1 + 4%)^17

= 10,400(1.04)^17

accumulated value = 10,400 x 1.9479 = $20,258.16

b)

when interest rate(r) = 6%

3 years:

future value = present value(1 + r)^n

here r = 6%

n= 3 years

present value = $10,400

so future value = 10,400(1 + 6%)^3

= 10,400(1.06)^3

Accumulated value = 10,400 x 1.191016 = $12,386.57

7 years:

future value = present value(1 + r)^n

here r = 6%

n= 7 years

present value = $10,400

so future value = 10,400(1 + 6%)^7

= 10,400(1.06)^7

Accumulated value = 10,400 x 1.50363 = $15,637.75

17 years:

future value = present value(1 + r)^n

here r = 6%

n= 17 years

present value = $10,400

so future value = 10,400(1 + 6%)^17

= 10,400(1.06)^17

Accumulated value = 10,400 x 2.692773 = $28,004.84

when interest rate(r) = 8%

3 years:

future value = present value(1 + r)^n

here r = 8%

n= 3 years

present value = $10,400

so future value = 10,400(1 + 8%)^3

= 10,400(1.08)^3

Accumulated value = 10,400 x 1.259712 = $13,101

7 years:

future value = present value(1 + r)^n

here r = 8%

n= 7 years

present value = $10,400

so future value = 10,400(1 + 8%)^7

= 10,400(1.08)^7

Accumulated value = 10,400 x 1.713824 = $17,813.47

17 years:

future value = present value(1 + r)^n

here r = 8%

n= 17 years

present value = $10,400

so future value = 10,400(1 + 8%)^17

= 10,400(1.08)^17

Accumulated value = 10,400 x 3.70001805 = $38,480.18

c)

It can be clearly seen that when interest rates are high future values or accumulated values are in increasing trend. i.e., more the interest rates more the future values

and also when the time period (depositing period) increases accumulated balance also increases.