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# (a) What sum of money will be required to discharge a loan of Php 7,800 on April 1, 2012, ?

(a) What sum of money will be required to discharge a loan of Php 7,800 on April 1, 2012, if

the loan is made on Oct. 1, 2003 at a rate of 9% compounded quarterly? (b) if the loan will be

paid semi-annual within the same period, how much will be its equivalent payment?

### 1 Answer

Relevance
• that is 1 Q in 03, 4 Q in 04 thru 11, 1 Q in 12 for a total of 34 quarters.

A = P(1+(r/4))^(4n)

A = 7800(1+(0.09/4))^(34) = 16620.63

Mortgage payment

A = P•r(1 + r)ⁿ / ((1 + r)ⁿ – 1)

A = 7800(0.09/2)(1 + 0.09/2)^(34/2) / ((1 + 0.09/2)^(34/2) – 1)

A = 7800(0.045)(1.045)^(17) / ((1 .045)^(17) – 1)

A = 7800(0.045)(2.1134) / (2.1134 – 1)

A = 7800(0.045)(2.1134) / (1.1134)

A = 666.24

total paid = 17•666.24 = 11326.08

Mortgage payment

A = P•r(1 + r)ⁿ / ((1 + r)ⁿ – 1)

A  is the periodic amortization payment

P  is the principal amount borrowed

r  is the percentage rate per period; for a monthly payment,

take the Annual Percentage Rate (APR)/12

n  is the number of payments; for monthly payments over 30 years,

12 months x 30 years = 360 payments.

Interest compounded quarterly

A = P(1+(r/4))^(4n)

r is annual rate as a decimal

P is principle

n is number of years

A is present value

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