Question

A $21,000 car loan is repaid with one payment of $26,533.47 after 36 months. What is the annual effective discount rate? Round your answer to 3 decimal places.

The effective annual rate of discount has been 6% for the last 3 years. Prior to that it was 5%. A bank account has a balance of $550 today. A single deposit of $X was placed in an account 8 years ago. Calculate the value of X.

Given that i^(m) = 0.216772 and d^(m) = 0.213467, find m. Give your answer as the nearest integer.

Answer 1

Part A:

Assuming it is monthly compunding.

Future Value:
FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$     21,000.00
Future Value	$     26,533.47
Periods	36

Future Value = Cash Flow * ( 1 + r )^n
$ 26533.47 = $ 21000 ( 1 + r ) ^ 36
( 1 + r ) ^ 36 = $26533.47 / $21000
( 1 + r ) ^ 36 = 1.2635
( 1 + r ) = 1.2635 ^ ( 1 / 36 )
( 1 + r ) = 1.00651794
r = 1.00651794 - 1
r = 0.00651794 i.e 0.651794 %

Annual Effective Rate:

Particulars	Amount
Ret period	0.651794%
No. of periods	12.0000

EAR = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.006518 ) ^ 12 ] - 1
= [ ( 1.006518 ) ^ 12 ] - 1
= [ 1.0811 ] - 1
= 0.0811
I.e EAR is 8.11 %

r - Int Rate per period

n - No. of periods per anum

Part B:

FV = PV ( 1 +r1)^n * (1+R2)^n

550 = X * ( 1 + 0.06)^3 * ( 1 + 0.05)^5

= X * 1.06^3 * 1.05^5

= X * 1.191016 * 1.276282

= 1.52007 X

X = 550 / 1.52007

= $ 361.825

Amount deposited 8 years back is $ 361.825