Question

Melanie invested $63,000 in an account paying an interest rate of 7\tfrac{1}{8}7
8
1
​
% compounded quarterly. Lillian invested $63,000 in an account paying an interest rate of 7\tfrac{3}{8}7
8
3
​
% compounded continuously. After 15 years, how much more money would Lillian have in her account than Melanie, to the nearest dollar?

Answer 1

Answer:

  $8727

Step-by-step explanation:

The difference in investment values can be found by computing the value of each investment, then finding the difference. Here, we're concerned with investments compounded quarterly and compounded continuously.

a)

Melanie's investment value is computed using the formula ...

  FV = P(1 +r/n)^(nt) . . . . where P is the principal, r is the annual rate, t is the number of years

  FV = $63,000(1 +0.07125/4)^(4×15) = $63,000(1.0178125^60)

  FV = $181,721.94

__

b)

Lillian's investment value is computed using the formula ...

  FV = Pe^(rt)

  FV = $63,000·e^(0.07375×15)

  FV = $190,449.05

__

c)

The amount more that Lillian has is ...

  $190,449.05 -181,721.94 = $8,727.11

Lillian has about $8727 more than Melanie.

_____

Additional comment

The interest rates expressed as decimal values are ...

  7 1/8% = 0.07125

  7 3/8% = 0.07375