Question

1) Please solve for the question marks (round to the nearest whole number where applicable):

  P.V. Years Interest Rate Compounding F.V.

A) ? 5 14% Monthly $3,725

B) $235 2 ? Semiannual $935

C) $6,250 8 6 3/4% Simple ?

D) $3,750 ? 3 1/2% Annual $8,315  

E). $1,075. 3   19% Weekly ?

F) Explain the differences between simple and compounded interest rates in light of the results you attained.

Answer 1

A) The basic formula is

PV * (1 + r)^n = FV

Here r = 14/12 = 1.167 % and n = 5*12= 60 ( since it is monthly compounding )

So, PV * 1.01167^ 60 = 3725

PV= 1857.29 or 1857 (rounding)

B)

PV * (1 + r)^n = FV

n= 2*2 =4

So, 235 * (1+r)^4 = 935

or (1+r)^4 = 3.9787

r = 41.2329%

This is the semiannual rate so the yearly rate = 41.2329 * 2 = 82.4658 or 82.47 %

C)

Simple interest rate = 6.75%

Interest per year = 6.75% * 6250 = 421.875

Interest for 8 years = ​​​​​​ 421.875 * 8 = 3375

Future value = 6250 + 3375 = $ 9625

D)

PV * (1 + r)^n = FV

3750 * 1.035^n = 8315

or 1.035^n = 2.2173

n = 23.1474 or 23.15 years

E)

Interest per year =19%

Weekly interest (r) = 19/52 = 0.3654%

n = 3*52 = 156

PV * (1 + r)^n = FV

or, 1075 * 1.003654^156 =FV

FV= 1898.91 or 1899

F)

Simple interest will yield lower future value than compound interest. This is because simple interest gives interest only on the initial principal amount throughout its period, whereas in compound interest the accumulated interests are added to the principal for calculating interest in the subsequent years.