Question

 Leslie​ Mosallam, who recently sold her​ Porsche, placed $10,400 in a savings account paying annual compound interest of 6%.

A.  Calculate the amount of money that will accumulate if Leslie leaves the money in the bank for 2, 6 and 16 years.

B. Suppose Leslie moves her money into an account that pays 8% or one that pays 10% REWORK part A. using 8% and 10%.

C. What conclusions can you draw about the relationship between interest​ rates, time, and future sums from the calculations you just​ did?

Answer 1

(A) Present Value = P = $10400

Interest Rate = r = 6%

Let number of years be n

Future Value = F = P(1+r)ⁿ

when n = 2, F = 10400(1+0.06)² = $11685.44

when n = 6, F = 10400(1+0.06)⁶ = $14752.60

when n = 16, F = 10400(1+0.06)¹⁶ = $26419.66

(B)

Present Value = P = $10400

Interest Rate = r = 8%

Let number of years be n

Future Value = F = P(1+r)ⁿ

when n = 2, F = 10400(1+0.08)² = $12130.56

when n = 6, F = 10400(1+0.08)⁶ = $16503.49

when n = 16, F = 10400(1+0.08)¹⁶ = $35629.80

Interest Rate = r = 10%

Let number of years be n

Future Value = F = P(1+r)ⁿ

when n = 2, F = 10400(1+0.10)² = $12584

when n = 6, F = 10400(1+0.10)⁶ = $18424.23

when n = 16, F = 10400(1+0.10)¹⁶ = $47787.72

(C) As the interest rate increased the future sum increases and as the time increases the future sum increases