Question

In: Finance

At a certain interest rate compounded annually, P5,000 will amount to P10,795 in 10 years. What...

At a certain interest rate compounded annually, P5,000 will amount to P10,795 in 10 years. What is the amount at the end of 15 years? Answer: P15,861.40

Solutions

Expert Solution

1) Calculation of interest rate

Future Value:
FV = PV (1+r)^n
Where

r is Int rate per period
n - No. of periods

Particulars Amount
Present Value $        5,000.00
Future Value $     10,795.00
Periods 10

Future Value = Cash Flow * ( 1 + r )^n
$ 10795 = $ 5000 ( 1 + r ) ^ 10
( 1 + r ) ^ 10 = $10795 / $5000
( 1 + r ) ^ 10 = 2.159
( 1 + r ) = 2.159 ^ ( 1 / 10 )
( 1 + r ) = 1.08
r = 1.08 - 1
r = 0.08 i.e 8 %

2) amount at the end of 15 years  

Amount after 10 years = $ 10795

balance period = 5 years

Particulars Amount
Present Value $          10,795.00
Int Rate 8.0000%
Periods 5

Future Value = Present Value * ( 1 + r )^n
= $ 10795 ( 1 + 0.08) ^ 5
= $ 10795 ( 1.08 ^ 5)
= $ 10795 * 1.4693
= $ 15861.4

amount at the end of 15 years = $ 15861.4

Please comment if any further assistance is required.


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