Question

SW1 compound interest (Compatibility Model - Word DESIGN PAGE LAYOUT REFERENCES MAILINGS REVIEW VIEW A man deposited P5.002 on the date his son celebrated his 1st birthday. If money is worth 10% compounded semi-annually, what is the maximum amount the son can withdraw on his 21st birthday? 1. You have a choice to borrow P5.000 from a friend or from a bank. The bank charges 20% per year while your friend charges 16% per month, the loan is payable in one year, where will you borrow to get the better deal and why? A. from the bank: I will save P1,04g c. tom the friend: I will save P139 B. from the bank: I will save P139 D. from the friend: I will save P1,049 2, 3, How long will it take to double the sum of money at 5% annual percentage rate? P7500 is deposited in a savings account at 6.5% rate of interest compounded quarterly for 25 years. Determine the accumulated sum. 4, 5, What is the original price of P1.zda5a discounted price at 22% discount? If P12,50Q is invested at 6% from January 1, year 1, how much money accumulated until January 1, year 10? 7- If P400 is deposited now in a savings account with an interest of 8%, what will be the value amount in the account in 8 years from now? 8. In how many years will the amount of P10.0002 triple if the invested at an interest rate of 10% compounded per year? 9. Today an investor withdraw P50,000 representing the accrued amount of his investment that matured. If he invest at 10% semi-annually for 10 years, how much did he invest in pesos? 10. A loan for P50,000 is to be paid in 3 years at the amount of P65,000. What is the nominal rate that is compounded monthly? continuousy

Answer 1

Solution

Back-up Theory

If a sum, P, is invested for T years at an interest rate of r% (or equivalently i in decimal form) per annum, compounded annually,

Amount at the end of T years, A = P(1 + i)^T ………………………………..(1)

Interest, C = A – P = P{(1 + i)^T – 1}…………………………............……..(1a)

If a sum, P, is invested for T years at an interest rate of r% (or equivalently i in decimal form) per annum, compounded semi-annually,

Amount at the end of T years, A = P{1 + (i/2)}^2T …………………………..(2)

Interest, C = A – P = P[{1 + (i/2)}^2T – 1] ………………………....………..(2a)

If a sum, P, is invested for T years at an interest rate of r% (or equivalently i in decimal form) per annum, compounded quarterly,

Amount at the end of T years, A = P{1 + (i/4)}^4T ………………………..(3)

Interest, C = A – P = P[{1 + (i/4)}^4T – 1] ………………………………..(3a)

Now to work out the solution,

Q1

Here, P = 5000, r = 10 and so i = 0.1, T = 20 years [number of years from 1^st birthday to 21^st birthday]

Compounding semi-annual.

Vide (2), amount = 5000(1.05)⁴⁰

= P35199.44 Answer

Q3

Let invested sum be P and time required to double be T years. Given, r = 5%, assuming annual compounding, vide (1),

P(1.05)^T = 2P, Or

(1.05)^T = 2

Taking logarithm on both sides,

Tlog1.05 = log2, Or

T = log2/log1.05

= 0.30103/0.0211893

= 14.21 years Answer

Q4

Here, P = 7500, r = 6.5 and so i = 0.065, T = 25 years, Compounding quarterly.

Vide (3),accumulated amount = 7500(1.01625)¹⁰⁰

= P57593.88 Answer

Q5

Let the original price be P. Then, discounted price = 0.78P [22% discount => discounted value is 0.78]

Given, discounted price = 1743759, the original price = 1743759/0.78

= P2235588.46 Answer

DONE